Theological argument has to be about the unprovable
Arguments about the Virgin Birth became serious only after the mid-19th century, when it became obvious that it was a scientifically impos sible doctrine. Since then, however, it has been one of the test cases distinguishing liberal or scientifically informed Christianity from the other sort. The Resurrection may be still more counter-factual, but it's not gratuitous or unnecessary in the style of the Virgin Birth, which seems something quite irrelevant to the central Christian message and can easily be explained away as a mistranslation.
It is not quite biologically impossible for a woman to give birth to a daughter without fertilisation, but it would be impossible for a female mammal to produce a son who was a clone (which a virgin birth would require). I know an evangelical Christian biologist who produced proof that, with two exceedingly unlikely mutations, a woman could give birth to a biologically female child who was externally a man. But it is hard to see the point. Simpler to conclude that science says it couldn't happen.
This kind of argument misses what is surely the most important and interesting thing about theological argument, which is its continuing popularity. Why should anyone care about questions which cannot, by their nature, be answered in this world? If we discount the explanation that all religious people are insane in proportion to their religiosity, and that religious ideas display a peculiar, contagious form of insanity, it is not obvious what might account for this.
So here's an idea: theological disputes are not often popular, but when they are, it is precisely their undecidability that makes them so. Most questions of a political nature have some kind of factual answer, and give an unfair advantage to the side that has more clearly grasped the underlying facts. The dispute between communism and capitalism was eventually resolved by the economic and political inefficiencies of communism.
Yet a dispute over the Virgin Birth, the nature of Christ, or the inerrancy of the Koran cannot be resolved by empirical means - which makes it an extremely pure test of political po wer and skill.
If you believe that the purpose of argument is to resolve factual disputes, this makes no sense at all. But few arguments, even among scientists, are solely about resolving disputes; the most bitter disagreements are those where no obvious experiment would settle matters.
Seen in this light, the Virgin Birth is an almost perfect doctrine. To force your opponent to deny or to affirm it is a test of rhetorical skill and ruthlessness. The same goes with greater force for disputes about the creeds or nature of Christ. For two or three centuries, the Byzantine empire was riven by disputes over the nature of Christ - was He of one substance with God, or were they two? The Greek terms differ by precisely one iota, yet the power struggles that they made possible were real and deadly enough. You say hom oousios and I say homoiousios, but each of us is trying to get the other to say "uncle".