Well, it is ambiguous...
This is because of the different meanings of "anti" in composite
words. Please have a look at
http://www.perseus.tufts.edu/cgi-bin/resolveform?lang=Greek using as search terms "anti" and "gonos". "Antigone" is a feminine
form of "Antigonos" (latinized="Antigonus")
Considering the tragedies about Antigone and her father both meanings
may apply, i.e. "like her father/mother" or "against birth". I would
say that this "against birth" actually means "against
family/genus(=clan)"
"Against birth" may also mean "against her own sex". Considering that
Antigone defied king's orders, she did something opposite
to her position as woman (as perceived in ancient times).