Canto 1 - Boyhood
Bāla-kāṇḍa
Chapter 36: Umā Curses the Demigods
Text 1.36.20

तदग्निना पुनर्व्याप्तं सञ्जातः श्वेतपर्वतः।
दिव्यं शरवणं चैव पावकादित्यसन्निभम्।
यत्र जातो महातेजाः कार्तिकेयोऽग्निसम्भवः॥

tad agninā punar vyāptaṁ sañjātaḥ śveta-parvataḥ
divyaṁ śara-vaṇaṁ caiva pāvakāditya-sannibham
yatra jāto mahā-tejāḥ kārtikeyo ’gni-sambhavaḥ

tat = that powerful semen; agninā = by that fire; punaḥ vyāptam = when was pervaded; sañjātaḥ = was formed; śveta-parvataḥ = a white mountain; divyam = a divine; śara-vaṇam ca eva = a thicket of reeds; pāvaka-āditya-sannibham = resembling the fire of the sun was formed; yatra = from that thicket; jātaḥ = appeared; mahā-tejāḥ = of great powess; kārtikeyaḥ = Kārtikeya; agni-sambhavaḥ = born of Agni.

A white mountain was formed when that powerful semen was pervaded by that fire. Over time, a thicket of reeds resembling the fire of the sun was formed. From that thicket appeared Kārtikeya of great prowess, born of Agni.

Kārtikeya is considered the child of the Kṛttikā goddesses because they fed him breast milk. Because he was held and given away by Agni, he is considered to have been born of Agni.