Hi! There are so many versions of the story of Kartikeya's birth, but that is what makes these things so interesting, hai na? So i know I can't be saying - here is the "right" one, but the version in the Shiv Puran is very layered and interesting, and shows the complexity of creation in this universe.
You know when Shivji and Mata Parvati finally are married and go back to Kailash they are absorbed in their physical union for very long time. The devtas become increasingly nervous as Tarkasur is still running free and no one can stop his atrocities. They are waiting and waiting for the divine couple to produce a son but no son has arrived as Shiv is a supremely self-controlled yogin and does not allow his seed (sorry😕) to flow downward. He is able to control all this.
So finally the devtas decide they must do something to encourage the couple to produce a son.. They go to Vishnu, who is the only one who is willing to approach Shivji on Kailash. A full kalpa had passed and no one had seen or heard from him! Vishnu comes up and shouts at the door, breaking the loving trance of Shivji ad Parvati. Shivji, in stirring himself to answer Vishnu's call, loses his concentration and spills his seed (again, sorry). This is a catastrophe as it was meant to be spent into Parvati's womb, so now how will there be a son? In this puranic version of the story, Agnidev turns into a bird and swallows this seed, but it burns him horribly, such is its power. It is the fire that can even consume fire.
When Agnidev can no longer keep this seed within himself, he ejects it (vomits it) and its heat is absorbed by the wives of the saptarishis - all except Arundhati, who had not come near the holy fire for warmth and so was not impregnated. They too cannot bear the pain and burning of this holy power and are tortured by trying to bear it. In the end, rejected by their husbands (as they are looking pregnant), they all vomit up this seed as well and it all flows together into a single womb-child. There it lay for a while, but even Himalaya could not bear its weight, so he flings it into the sara grass along the banks of Ganga.
This womb-child lays on the banks of Ganga for another kalpa, and then, with thunderous rumble, there is all of a sudden there a beautiful boy.
He begs Visvamitra to perform auspicious rites over him. And then the Krittikas, attracted by his glow, come to earth and fall in love with this boy at first sight. they each one give him milk form their breast. He even produces six heads so he can drink from all at once and they will not argue over him! These krittikas take him to the stars and care for him and raise him lovingly.
Meanwhile, Shivji and Parvati after long want to know what has become of this seed, which cannot ever fail - so what has become of its creative power? Arrey - now the whole story coes out. Bhoomi tells that the seed has fallen upon her and she could not bear it. Then Agni explains, then he too tells of the rishis wives. Himalaya tells his part, and Ganga explains she could not bear this heat and it stayed in the grass on her banks. And they tell that, in this grass, it became a wonderful boy. The devtas know that the krittikas have this boy.
The shivgans go to the krittikas and beg for the boy. They explain to Kartikeya who he really is. He agrees to go, but his dhai-maas are so heartbroken that he brings them along.
Shiv greets him and kisses him and brings him to Kailash, where Parvati, taking him in her lap, gives him milk from her own breast.
He is installed thus as their true son. But, in a way, he was raised by the whole universe, which in turn make sense as that is exactly who Shivji and Parvati really are.