Her entire purpose as a biological weapon was hunting down the "strongest" man she could to give her children, to wipe out humanity. After finding something "off" or being interrupted during all her previous attempts at mating, she eventually singles out one of the team that's been causing her all the trouble, because the fact they even could shows a certain kind of strength the other men all lacked (power/authority). Plus she was just getting desparate.
But you should watch it again. She's an alien weapon, and her function is to f**k, get preggers and wipe out and/or replace humanity.
