In both cases, it's parents who want to protect what they see as their rights I suppose. Either the right to not be lumbered with a child they don't want or, not to lose the child they invested time, money and love in.
Just pratically speaking too- there's more about a person to grieve for once it has been born, lived here for a while and, interacted with people. I agree though, I don't like this idea that our lives belong to other people.
The abortion issue is a complex one I think. When is it considered a life that has rights? Rights that equal the mothers? I do understand people saying that- when it's a fetus, it's simply a kind of unfeeling group of cells. It doesn't have the ability to choose anything. It isn't even conscious. Still- it surely still does have some rights. Maybe they aren't legally protected quite as much as an adults. But- say the mother chooses to continue to smoke, take drugs or drink alcohol excessively. She'll most certainly be looked down upon if those things harm her baby. I suppose that is conditional on her doing those things while she still intends to have the baby.
I find it kind of weird though in a way. The whole- 'My body, my choice' thing. Like a baby is a fashion accessory or tattoo or something you can get removed if you go off the idea. That abortion becomes a kind of belated contraception. It just sounds kind of flippant. But still, that's probably in part because I have old fashioned, prudish ideas around sex itself. It's not something that appeals to me as a flippant thing to do. That's not to say I think other people shouldn't. It's just a personal bias. I guess there are all sorts of reasons a person could become pregnant though.
That said- I am pro-abortion. I don't think it's fair to bring a child here that isn't wanted in the first place. It might work out ok for them I guess but I feel like the risk factor for things going wrong increases.