Roe vs. Wade being overturned means that the policy on abortion reverts back to the states, the way your constitution states things which are not regulated by it are to be decided. Some states will continue to offer late-term abortions, some will move to a model more comparable to that in much of Europe with 1st term elective abortions being legal, others will move to ban elective abortions altogether.
The emphasis on his is not as telling as you make it out to be given that fathers also play a role in the conception (by definition) and raising (hopefully) of children. Some men will see what they considered to be their "right" to skip the consequence of them having intercourse without contraception taken away. Those who consider elective late-term abortion to be an essential part of life may move to those states which continue to provide this - New York and California seem to be poised to become abortion 'free states' - while those who consider abortion to be an abomination/against their religion/... may move to those states where it is limited. As far as I know - and correct me if I'm wrong - there are no states where abortion in case of rape or incest or in those cases where the life of the mother is directly threatened is forbidden.