Well I'm not a lawyer so I really can't do that answer justice, but from what I gather of this situation he's claiming that him being anti-choice ("pro-life") as the primary reason he doesn't want the embryos destroyed and has claimed two ex-girlfriends had abortions to which he vocally opposed at the time & that the second abortion in particular has had a lasting negative impact on him mentally. So by forcing him to name the exes her team are (a) authenticating that women actually exist (b) confirming that they did, indeed, have abortions and (c) that he was as militantly anti-choice and vocally opposed to those abortions that he claims he was and that he claims to be now.
And from there (even if all else falls through) Sofia has the argument that those women weren't forced to mother his children, so why should she be? Why were they afforded the right to dispose of their embryos but she isn't?
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