I've never understood the silly pro-choice v pro-life debates?

Why can't one be both pro-choice and pro-life. I mean after watching an abortion just take place yesterday(7 mnths), i really fely i was witnessing some of the most gruelsome times in my life. The doctors and the medical staff just ignored the baby as it was crying. I have always been against laws banning abortion or criminalizing it, but after this I can see why some people try to legislate on it. But wouldn't it be a better idea if the babies aborted after a certain date or trimester were kept in that cube box(i cant remember the name) and given up for abortion when they reach proper birth age. Wouldn't that solve a lot of these problems and put some kind of an end to this debates