The child had his birth from the action of Rudra entering into the constitution of the deity of fire and for this reasort Skanda is called the son of Rudra.
अनुप्रविश्य रुद्रेण वह्नि जातो ह्ययं शिशुः। तत्र जातस्ततः स्कन्दो रुद्रसूनुस्ततोऽभवत्॥