By rights, one means an entitlement a person has to do something.
Abortion, on the other hand, does not concern the pregnant woman doing something. People don't do abortions on themselves. Rather, abortion, as it is usually understood, refers to the act an external party, the doctor, performs at an external location, the hospital, all made readily available by yet another external party, the government. Further, there are costs and logicistal issues associated with this entire procedure, which, again, are external matters.
Hence, why is abortion usually spoken of as if it is a right, when it involves primarily other people doing something, and hence does not only fail to meet the definition of a right, but actually seems to be the opposite of a right?
Imagine, for example, a world in which nobody wishes to perform an abortion on somebody else. In this hypothetical world, abortion cannot possibly be a right. It would be self-contradictory, since it would be a right that would restrict everybody else (mainly: everybody's right to not be forced to perform abortions against their will).