This abstruse subject has become the center of many sordid controversies, in our times.
The first thing to be understood is that there are many versions of the birth of Gaṇesh.
Apparently, his birth takes place differently in different Kalpas.
This itself is a very recondite & difficult issue, because it’s difficult to see any value in knowing the birth of anybody in another Yuga or Manvantara, let alone another Kalpa.
I think the idea of these time-cycles is a very deep Yogic mystery, which I’m not competent to write about.
We shall confine ourselves to the present Kalpa known as the Shveta Kalpa, in which Gaṇesha’s head is cut off by Shiva.
A very clear & detailed account is provided in the Shiva Purāṇa, but there seem to be many variations of this account too.
I’ll base my comments on the broad legend as known to all, and as it exists in popular, public imagination.
To begin with, it should be very clear that there are multiple interpretations of any of these ancient legends {in any part of the world, not just India}.
Confining myself to the Shveta Kalpa and the Shiva Purāṇa, I’ll also confine myself to only one possible interpretation.
It is largely a cautious guess, and I can’t possibly claim originality of perspective.
My perspective has been shaped by a couple of other thinkers, and I share my thoughts for what they’re worth.
Basically, the conflict between Gaṇesha and Shiva reflects the conflict between the Supremacy of Prakṛti and the Supremacy of Puruṣa.
It is implicitly a war between Pārvatī and Shiva.
This is both metaphysical and historical.
This war has been fought both at an ideological level, and at a political level.
At a historical-political level, it actually does seem to indicate a conflict between “Father-God” and the “Mother-Goddess” cults.
While the former can be called “Patriarchy”, it is questionable the extent to which the latter can be called “Matriarchal”.
At any rate, the Mother-Goddess reigns supreme, and Goddesses in general, were more powerful & popular, in this cult.
The extent to which it can be called Sānkhya is also doubtful, but there’s a very strong probability.
Simply put, Shiva represents “God” or Puruṣa.
Pārvatī, his consort, represents Prakṛti.
That Gaṇesha is produced either from Pārvatī’s body, or from some ointment or paste to be smeared on her body – {are all minor variations} – basically indicates Parthenogenesis, or the birth of the Son-God, i.e. the Cosmos, without a Father.
This basically means that there is no Supreme Spirit {Shiva-Puruṣa} underlying the Universe – everything comes from Nature {Pārvatī- Prakṛti} itself.
Pārvatī creates Gaṇesha because Shiva always makes his way in, without really caring about her consent.
She has no autonomy – or, at any rate – any real autonomy.
On a social level, this means the Male is all-independent and willful.
The Female is subordinate.
Gaṇesha represents a revolt against this idea.
He has been set up by the Mother-Goddess as a refusal of the absolute dominion of the Male-Father-God.
He belongs entirely to the Mother.
Gaṇesha refusing Shiva entry into his own house, appears to be an allegorical representation of the Mother-Goddess-cult’s refusal to accept the supremacy of Puruṣa – or, to say the same thing – his absolute independence from Pṛakrti.
{The questions being...
Does Prakṛti create the universe alone?
Does Puruṣa need Prakṛti to create the universe?
Does Prakṛti have to depend wholly on Puruṣa, for creation?
And so on.}
He doesn’t “know” Shiva either – i.e. he actually doesn’t recognize the existence of Puruṣa, or the Underlying, Substrate Spirit of the Universe.
Shiva’s cutting off his head allegorizes the defeat of this cult.
The supremacy of Spirit over Matter.
It should be noted that Gaṇesha’s strength is reinforced by the Shaktis in the narrative, and he is finally called “Shakti-putra” {28, Ch.16}.
Pārvatī herself aids Gaṇesha in his combat with the Gaṇas of Shiva, and creates Shaktis from herself, who assist Gaṇesha.
“44 In the meantime, goddess, the mother of the universe, of special knowledge, came to know of the entire incident and was very furious.
45 O great sage, the goddess created two Śaktis then and there for the assistance of her own Gaṇa.
46 O great sage, one Śakti assumed a very fierce form {pracaṃḍa-rūpa} and stood there opening her mouth as wide as the cavern of a dark mountain {“vistīrya mukhagahvaram”}.
47 The other assumed the form of lightning {“vidyutsvarūpā”}.
She wore many arms.
She was a huge and terrible goddess {“bhayaṃkarā mahādevī”} ready to punish the wicked.
48 The weapons hurled by the gods and the Gaṇas were caught in the mouth and hurled back at them.
49 None of the weapons of the gods was seen anywhere around the iron club of Gaṇeśa. This wonderful feat was performed by them.”
{Chapter 15, Book 2.4 - Rudrasaṃhitā, Kumārakhaṇḍa}
Finally, of course, Shiva decapitates the Son of the Goddess, the production of “para-māya” {13.18} – the Great Māyā – hence, Māyāvic himself.
His resuscitation, with the head of an elephant – and subsequent apotheosis as the chief of the Gaṇas, i.e. his own followers who are all presumably male – is a subtle allegory of the re-formation of the Mother-Goddess cult which now acknowledged the supremacy of the Spirit, or Puruṣa.
Gaṇesha is a resurrected god who is no longer a pure product or emanation of Pārvatī.
He is now also the son of Shiva, the Great Cosmic Spirit, of Puruṣa – and he is NOT a physical product of the Goddess.
His identity has undergone a fundamental change.
His {new} life comes from Shiva, not from Pārvatī.
The materialistic-atheistic point of view has lost.
The Father-Right has been established.
The Female, the Mother, has lost her autonomy.
Vedānta triumphs over Sānkhya.
But this doesn’t mean any insult to, or annihilation of, the Mother-Goddess cult.
Indeed, the allegorical story makes this point very clear.
Pārvatī, in rage at the death of her progeny, would have destroyed the universe, and so Gaṇesha had to be resurrected.
Nature cannot be humiliated or suppressed violently: such injury to Nature would destroy everything.
The female Shaktis emerge to be more powerful than the male Gaṇas of Shiva who are presumably representative of the higher, spiritual order.
That is, the elemental, bhautika realm of the Shaktis is powerful, irrepressible, & essential.
In other words, Matter or Nature cannot be killed or violated: it has to be subordinated & integrated.
The resurrection of Gaṇesha prevents the annihilation of the universe, but only after establishing the greater power of the Spirit.
Both Spirit & Matter are affirmed.
At a historical-political level, it seems to indicate a continuation of the old Mother-Goddess-with-her-Son cult, but reformed, modified, and integrated with the Patriarchal Father-Spirit-God cult.
{Or it may indicate, as noted, that there can be no creation only with Puruṣa, but Prakṛti is needed, even if she’s subordinate to Puruṣa.}
In other words, Gaṇesha is the Primordial Son-God of the Ancient Mysteries, born alone from the Mother-Goddess, with no intervention or role of the Father.
This cult portrays & worships the Mother & the Son: the Father is conspicuously absent.
That Gaṇesha is produced solely from the “dirt” {“mala”} of the Mother – which has also been interpreted as her menstrual-blood {quite accurately} – is also an allegorization of the cult in which the Father-Spirit was rejected.
If we were to agree with the theories of some radical freethinkers – like Gerald Massey – it would refer to a time when the role of the Father or Male in the actual birth of the child wasn’t recognized or understood, and the Mother was thought to be the sole producer of the child.
{Though, as I’ve written earlier, I find this theory unconvincing: the simplest observation of the animal world itself demonstrates the role of both male & female.}
Taken as a valid point, however, this makes the tale more literal, less symbolic {i.e. the initial creation of Gaṇesha represents the system in which the role of the Masculine-semen is unrecognized: it is only the menstrual-blood which produces the child in the womb}.
But we would rather say, that the social-political-cultural perspective is more accurate than the biological, and that the Father was irrelevant – or he was actually rejected – that in this system, the Mother reigned supreme, and the male was under the dominion of the Mother.
The Masculine-Principle is subordinated to the Feminine-Principle.
This is the more likely meaning.
When Gaṇesha refuses the Gaṇas to enter the abode of Shiva-Pārvatī – Shiva tells them {Chapter 14, Rudra-saṃhitā: Kumāra-khaṇḍa}:
“57 O Gaṇas, hear you all.
A battle may not be a proper course.
You are all my own.
He is Pārvatī’s Gaṇa.
58 But if we are going to be humble, there is likely to be a rumour: “Śiva is subservient {vaśya – under the control of/controlled by} to his wife {strī}.”
O Gaṇas, this is certainly derogatory to me.”
...
This is very, very clearly a struggle, not between Shiva and Pārvatī per se, but between the Supremacy of the Father {Spirit, Male, Semen} and the Supremacy of the Mother {Matter, Female, Menstrual Blood}.
Do note that the Spirit or Soul in India is called Puruṣa and Puṃs, both of which mean Male.
So the whole legend is a subtle allegory of the conflict between the Mysteries which were atheistic & materialistic, based on the worship of pure Nature, of “Mother Nature”, of the Ancient Mother Goddess, the Primordial Creatrix-Genitrix of the Universe – and the Patriarchal Cult which assigned supremacy to the Spirit.
P.S. A very long post-script!
Since there are other legends about the genesis of Gaṇesha, there are also other aspects/dimensions, and other interpretations possible – both of this allegory, and the others.
For one, I think I can discern a distinctly Yogic allegory here, but perhaps I shouldn’t write too prematurely.
Basically, Gaṇesha may represent the Yogī himself, who is finally “killed” by the Supreme Spirit {you could say, the Ātman} – i.e. his lower, elemental, egoic self dies – and he achieves transcendence.
The elephant-head signifies spiritual enlightenment or Yoga-power or transcendence {if not Mokṣa} – not a “beast”.
He is given a new identity & a new life by the Supreme Spirit {Shiva}, he is no longer a mere product of matter or body {Pārvatī}.
This is all I can surmise, for now, but it does go much deeper.
Fact is, the figure of Gaṇesha is deeply complex & metaphysical, since he is the same as Brahmaṇaspati of the Vedas.
This is strenuously denied by modern experts, but then Hindu revisionists do not agree with many ideas & conclusions of modern experts.
Otherwise they would not be revisionists.
Indeed, Gaṇesha may be called a form of Shiva-Rudra Himself.
There’s a peculiar passage in the Shukla Yajur Veda {3.57}:
“O Rudra, this is thine allotted portion.
With Ambikâ thy sister kindly take it.
This, Rudra, is thy share, the rat thy victim.”
...
Here, Ambikā has been called Rudra’s sister, rather than his wife.
{There’s no need to read human, biological incest into this.
These identities merge when the terms are understood as metaphysical or cosmological.
So, for instance, the Sun has been called the Son, the Brother, the Lover, and the Father, of Dawn.
Because the fact that Dawn {Uṣā} & the Sun {Sūrya} are essentially simultaneous & inseparable, but not identical, phenomena – allows the imagination to view their “relationship” in various ways.
It may be said that the Sun is the Cause of Dawn – there is a Dawn only because of the motion of the Sun – if there were no Sun, there would be no Dawn – in which case he’s the Father.
From another point of view, the Dawn strictly, in chronological order, precedes the actual rising of the {visible} Sun – and in that sense, she could be said to “generate” the Sun, and thus be called the “Mother” of the Sun.
From yet another point of view, they emerge simultaneously, out of the dark chaos of Night, and may be seen as siblings born together.
These views have tended to merge – and what arose were juicy, scandalizing tales of “incest”.
This incest is an imaginative, colorful, poetic, imaginative gloss – which hides the true significance of things.
Without entering into the possible meanings of the Shukla-Yajur-Veda hymn, one can say that if Rudra is Prāṇa, then Ambikā, as Vāk, can be called his “sister”.
Similarly, if Rudra is the Mind or Manas – then Ambikā, again as Vāk, can be called his “sister”.
At the same time, they can be viewed as “husband & wife”, because it is from their interpenetration that the world of phenomena, or life, or material consciousness, arises.
The point, however, to be made, is different.}
The original verse says “pashu” – which means “animal” – Griffith has translated this as “victim”.
Fact is that some ideas behind this verse can be found in the Shatapatha Brāhmaṇa.
Ambikā is called the sister of Rudra in that text too.
There’s at least some reason to think that the rat is being given an offering, but I’m yet to dig deeper into these strange verses.
It’s astonishing that such early Vedic texts tell us that the rat {“ākhu”} is Rudra’s animal.
Whether a “victim” or not, it is an animal that’s specially assigned to him.
In Non-Vedic literature, this concept has been translated into the symbol of the rat-vāhana of Gaṇeśa.
It also means that in the deepest esoteric sense, Ganeśa is not different from Shiva-Rudra, or is an aspect of Shiva-Rudra.
In the Shukla-Yajur-Veda hymn, the Mṛtyuñjaya-jāpa follows at Verse 60.
That’s all I can say, for now.