Well, it's also about women and how historically men have controlled what they do with their bodies, particularly with respect to reproduction.
Not fundamentally. If abortion
was murder, it wouldn't matter how lengthy a list of grievances you could bring on behalf of women, it'd still be murder. It wouldn't matter who was enacting the laws, they'd still be coherent with the generally accepted prohibition on murder. The debate around the morality of abortion hinges on whether abortion is or is not the killing of a human person with their own little bundle of rights and protections, and at what point a foetus crosses that line.
The historical control exercised by men over women's reproductive freedoms is certainly an issue worth confronting, and it's important in tying together the struggle for abortion rights to issues like access to contraceptives, the provision of effective sex education, and so on, to the whole progressive program of equality and freedom and all that good stuff, but it's not central to the narrow issue of whether or not abortion is or is not moral.
It fundamentally is, certainly at least on the pro-life side. The pro-choice term, though, is a very poor choice of words, then. And especially of the arguments I see in their rhetoric.
I don't know what to call the 'I think the early fetus isn't a person, ergo I don't mind if it's killed' position. It's my position, certainly. But I always thought the pro-choice position was that it was the woman's choice on whether her womb was being used against her will. It's where so much of the argumentation lies.
That seems like an issue of phrasing. We could also say "I think the early foetus isn't a person, so it's the woman's choice to terminate". The reservation you have around the term "choice" seems rooted in an over-literal meaning of the word as describing an absolute and unrestricted liberty, which is, aside from anything else, at odds with how people use the word in day-to-day life.
By analogy, I can drink a beer, because that's my choice, and anyone seeking to prevent me from doing so would have to have a good reason to constrain my choices. But if I was a severe alcoholic, if that choice becomes destructive, then people have reason to intervene, to constrain my choices. So it's possible for a person to oppose the prohibition of alcohol on "pro-choice" grounds, while still accepting the need for intervention to prevent self-harm. (Not a perfect analogy, I'll grant you, because there's obviously a difference between self-harm and harming somebody else, bu you see the point I'm making.) The question is always where the line is drawn where we permit that kind of intervention, and in this case, most pro-choice advocates accept foetal sentience as the most reasonable place to draw it.
I'll acknowledge, some people do lean heavily on the argument from bodily autonomy, and if made too crudely, it leads to some questionable conclusions. But I think these conclusions are generally unintentional, a result of poor or simplistic argument, rather than an opinion held by most advocates of abortions rights, or a necessary condition for identifying oneself as "pro-choice". If that was the case, "pro-choice" would describe a tiny fringe of ultra-libertarians, rather than the large, multi-national movement we generally take it as describing, and which you seem to support.