It is easy for me to be pro-choice because it is self-evident to me that a second-trimester fetus is not a person. For me, rights attain to what something actually is, not to what it might become; the fact that the fetus might in time become a person with rights does not mean it has those rights when the abortion is performed.
But the real reason I am "pro-choice" on the question of abortion is that I'm in favor of choice -- that is to say, freedom -- in general. Even if I accepted that the fetus counts as a full person, I am quite swayed by the argument by analogy that posits that I get mugged in a dark alley and wake up in a hospital bed with a person in the next bed tied to me by a bunch of tubes, and unless I stay hooked up for 9 months, the other person dies. I don't think there's an easy answer for whether I have to stay in your bed, but I don't think it's acceptable for someone else to decide for me and chain you down. Only I can decide how important it is for me.
A supporting argument for me is that I think all valid interests point to only having wanted children born. It's not fair to a child to be born to a mother who doesn't want it or who knows she isn't able to handle it. It's not fair to society to have to deal with the consequences of a mother's life shattered and a child raised unwanted. And the abortion occurs before the fetus is a person with an opinion or an interest. My contempt for those who would punish a woman for her sin with an unwanted child is boundless.