I have stood on both sides of the abortion debate. I was raised conservative. Most of my family is conservative. But I became more liberal as an adult. In listening to both conservatives and liberals argue their side of the debate they have something fundamental in common: both are motivated by a desire to care and protect. Liberals want to protect the rights, autonomy and health of women. Conservatives want to protect the life of the unborn.
Both sides see the other as monsters out to attack. They think that because the other side works to thwart their efforts to protect, that the other side intends harm. But that's not true. Neither side wants to inflict harm. They may be willing to inflict harm to protect another, but that is not the same as wanting to inflict harm. Those who are pro-choice don't want to kill babies; they want to protect women and sometimes killing the unborn is the unfortunate cost. Similarly those who are pro-life aren't necessarily motivated by a desire to control women*; they want to protect the unborn and limiting some rights of women is the cost.
* This of course comes with some sticky caveats. There is plenty of sexism among many who are pro-life, and plenty of hardliners who think women should be subservient. And those people's sexism does color there views of women's reproductive autonomy. But there are also moderate pro-lifers who otherwise value the rights of women. You don't have to be sexist to be pro-life. Anecdotally the pro-lifers I know personally are in the latter group.