No subject in American politics exhibits our reliance on strawman more than the abortion debate.
Pro-lifers hate women and want to control their bodies. Pro-choicers hate babies and care about their own convenience more than the lives of children.
Or, alternatively, pro-lifers honestly, truly believe that fetuses are children, in which case it is obviously the proper choice to restrict abortion. Pro-choicers honestly, truly believe that personhood does not begin at conception, in which case there's little room for abortion to be ethically wrong.
Until both sides start addressing each other's actual arguments, this subject is not going to cool off. You won't convince a pro-lifer who sees fetuses as children by wrongly claiming they want to control women. You won't convince a pro-choicer who sees personhood as developing later by insisting that they are a godless baby-killer.
Sidestepping the fetal personhood argument for the moment, the fact is that no one has a right to your body but you. You cannot be coerced to donate an organ, so it stands to reason that you also cannot be coerced to carry an unwanted pregnancy.
If the pro-choice movement focused on rhetoric like that more, I think it would have much more success. Of course, that's only if the pro-life people are receptive to having their minds changed.
It's a solid argument but the problem is that it concedes the fetal personhood argument which is far from settled. And conceding that point leads to a whole bunch of, frankly, nonsensical legal implications down the line (not just about abortion but about nearly everything) so it doesn't really make sense to move on from it.
Good luck with that. There's a very strong argument to be made that the so-called pro-life movement is thinly-veiled white supremacy with its roots in Brown v. Board of Education.
Apologies if that comes off as excessively bitter.