Our law does not consider those things equivalent and I bet if you went around and asked many people would not consider that equivalent either.

Naturally a society which practices abortion but not abandonment would think so. But in both cases the function is essentially to provide a mechanism for infanticide to a society in which infanticide is prohibited (or rather, abhorred). There is a rationalization (for us, that the fetus isn't a child; for them, that the child is not actually killed, its life being turned over to the gods or to fate) but the rationalization is secondary to the fact that the act leaves the parent within, or on the border of, the normal workings of society instead of outside them altogether.

I don't agree, but I think my argument would work equally well if we took the example of being born into slavery.

Or adoption. Or I mean... it's not like people don't still abandon their babies if they really want to.

You can even avoid legal consequences by abandoning them at a fire station: https://en.wikipedia.org/wiki/Safe-haven_law

Yes, but in the Roman world they left them at trash dumps and if they didn't simply die of exposure they were free for anyone to take as slaves. So I think we're still doing a bit better.

So... you're saying that society provides a more humane option so that we no longer leave children to die of exposure. Unlike in the past.