It is in fact up to the person carrying the baby (man, woman, or non-binary-identified), because it's *their* body and life on the line. This is actually argued and debated and analyzed exhaustively all over the place, both on- and off-line, so suffice it to say that the law is fairly clear on that point. It also specifies that abortion is illegal after the point of viability, which is when the fetus is able to survive outside of the womb. Nobody is actually performing abortions on 8-month babies. There are very VERY rare cases in which the baby is already dead and has to be removed before the mother dies of infection, which get mixed up into horror stories about murdering babies.
Personally, my mother said similar things about wishing she'd aborted to me, too. Of course, she's also Catholic and firmly believes in the Church's mandate that birth control is a sin... And she made it very clear that if I ever came home pregnant while I lived with her and wasn't married, she'd kill me. She wasn't kidding, either; not sure she'd risk the jail time except in the heat of passion, but this is the same woman who once threw me down a flight of stairs for mouthing off to her when I was 11, and hit me in the face with a wooden picture frame and knocked out a tooth when I was 4 - and that time was because she'd started shaking my two-year-old sister and I didn't want her to kill the toddler. She did heat of passion pretty well, and could accidentally have killed both of us. I don't doubt at all that she would have flown off the handle and I *and the fetus* might not have survived it if I'd admitted that I thought I was pregnant in college (turns out it was thankfully a false alarm). So there's a lot of nuance to these sorts of discussions, and approximately a million personal reasons why someone might choose abortion.
Myself, I have not known one single person who did it because of fear of jeopardizing a career, or got up one morning and decided they were bored with pregnancy, or any of the other "shallow" reasons that are often cited as accusations against people who have abortions. Of course, the catch is that depriving people of the right to abortion - or forcing them to meet some arbitrary standard in order to "earn" it - runs the risk of also penalizing anyone else who gets pregnant, even those that the person making the argument to limit it would agree were much less clear-cut cases. Like a lot of other legally granted rights, the fact that someone occasionally misuses it in someone else's eyes is the price of letting everyone choose.