AHA touts the parallel between abortion and slavery. If slavery could be abolished, so can abortion. But even though there are moral similarities, there are crucial differences.
Most folks didn't own slaves. It was basically an upper class thing. So most folks didn't have a direct stake in slavery. Just the ruling class, which was a tiny minority of the overall population. And in America (by the 19C), it was regionally confined.
In principle, it's a lot easier to abolish something that most folks never had or never use. You're not taking anything away from them. That's cost-free.
To the extent that there was a perceived stake in slavery, that's because an agrarian economic is labor intensive, and slave labor is a source of cheap labor.
Mind you, even from an economic standpoint, that's unnecessary. To begin with, slaves need to be fed and sheltered. So it's not free. Moreover, slaves are motivated to do the least they can get away with. So even apart from moral considerations, there are more efficient alternatives.
By contrast, there's a huge demand for abortion–national wide, from top-to-bottom. Many people want access to abortion at all social strata. And that includes a significant voting block.
That makes it far harder to abolish abortion. That doesn't mean we shouldn't try. But the facile parallel between slavery and abortion is politically disanalogous.
A better comparison would be Prohibition. That failed because popular demand was too great. Same thing with hard drugs. We can't eradicate substance abuse. The best we can do is to minimize it as much as possible.