Please don't take this as snarky--I'm genuinely interested (and you know my bias on this):
I would argue that supporting someone having a "choice" to perform a 21-week abortion is supporting that abortion. Is that not how you see it?
Well, holding up signs that say "abortion" isn't the same as holding up signs that say "pro choice". Because Pro choice means it's not for me to tell a woman what she can or can't do with her own body.
I'm pro choice, but I'm not in favor of abortions. I just believe that it's not for me to tell someone who isn't my wife or girlfriend, who I am not the father of the child, what to do with her own body.
And even if it is my own wife, I can't tell her what to do with her own body. I'd much rather she didn't have an abortion BUT I don't think the # of abortions that are just 'oops, didn't mean for that to happen' are has prevalent as others do.
Pro choice doesn't just mean 'abortion or not', in simple black or white terms (abortion on its own, isn't a black or white issue). There are health concerns you have to consider, both the mothers and the babies.
There are also people who are pro choice but would rather people put babies up for adoption if they can (i.e., healthy enough etc). But if you take away pro-choice, you pretty much make everyone who gets pregnant have to carry their pregnancy to full term.
In an ideal world, yeah, that would be good. but in the real world, no it's not.
I have two anecdotal cases here. A family friend was in her 40's when she got pregnant. It was a planned pregnancy, but she knew with her age (at the time) it could lead to health issues for the baby. She had the test done to see if there were any health issues with the baby, and there was (the baby would have down syndrome).
She chose to to have an abortion and while I didn't personally agree with her choice I supported her right to make the choice. As much as I didn't like the choice, nor felt comfortable with it, the pressure she was under (both in her own mind and her family) dwarfed any issues I had with it. What she needed was my support, and help. What she didn't need was me telling her that she can't make a choice on what to do with her own body.
Another case is a 2nd cousin of mine who had to have an abortion, because she had an ectopic pregnancy. Had she not had the abortion, she would've died.
In that case, I supported her choice and was glad it was a choice she was legally allowed to make.
I would never want to make that choice, but I would really never want to be denied the right to make that choice.
So thats why I think saying you're "pro choice" is not the same as saying you're "pro abortion". It's not the same, and it's just a simple way to demonize the argument.