Is God's Fatherhood a Metaphor?

I was really interested to discover in the tradition that early theologians are very comfortable saying like the eternal begottenness of the sun has some kind of paternal things going on. So I say, well, why couldn't we just call God parent? Because that would get the intimate relationship, but yet the differentiation between the father and the son. But we go with father because of the incarnation. It's like the incarnation allows us to see and gives us language for what was always true.