A gentile father is technically not the "father". Sure biologically yes but the child of a Gentile is a ben or bat Avraham. Because they have no biological and spiritual Jewish father-- the father automatically becomes Avraham.
Hashem forbade intermarriage. He said it is forbidden and in fact such relationships would take the Jewish person in the relationship away from Hashem. A Jewish child needs the guidance from their Jewish mom and their Jewish dad. Both of them are essential to the child's development into a religious and observant adult.
To give an example... a Kohen is set apart from Israel to work in the Temple. As such, Hashem required all Kohanim to bot be blemished. If a Kohen wants to marry a Jewish woman, both her parents needs to be Jewish. The mother and father must be Jews for the woman to be able to marry a Kohen. This may be a rabbinical prohibition but it's an example. If it's ok for Jewish woman to marry Gentile men- then why are Kohanim not allowed to marry the Jewish daughter of a Gentile man? That says something about the importance and seriousness of the situation.
I found this article that I found helpful:
http://www.aish.com/jw/s/100712764.html