The pro-choice side would say the by banning abortions you are infringing the right of a woman to choose when to have a child. The pro-life side would contend that by enabling abortions you are infringing the right to life of an unborn human. Both positions are framed in terms of human rights and plenty of "reasonable rational" people argue vigorously for each one while viewing those who disagree with them as basically evil.
Framing the debate in terms of individuals' rights is intended to remove the topic from the realm of political discussion and shut down dissent. It also completely drowns out discussion of the societal effects of allowing/banning abortion, which is just as important as the effect on individuals. The same unproductive dynamic plays out in the debate over e.g. the right to free speech.