It's always funny when people try to define terms and they try to rip off the style of dictionary entries despite not having the same mastery of English as dictionary writers. Just saying "born with the capability of holding eggs" didn't sound dictionary-y enough to her, so she tried to add more to make it sound more badass and legit. But saying anyone is born with the intention to hold eggs is the most ridiculous and obviously flawed part of her whole argument, which would have been better off if she just left it out. But nooooo I need to sound super smart.
A stronger play from here would have been to utilize the fact that Dani challenged her not to exclude any cis women, so you could just propose that the definition of biological female is identical to the definition of cis woman. This would include all cis women and exclude all trans women by definition, just like Lea wanted to do. And by using Dani's own terminology which Dani already implicitly agreed was valid, Dani is left without a clear counterargument. But Lea was too stupid to have this simple idea. And Dani was too stupid to realize that she was already implicitly agreeing to there being a substantive difference between cis and non-cis women worthy of terminological distinction, and that she was implicitly drawing a connection between biological women and cis women by putting forth the challenge in the first place. A profound display of inability to think from all sides.