I don't think that's where the front of any sort of meaningful battle lies, both are often a term of convenience or familiarity and not necessarily from an underlying agenda around abortion rights.
Further, attempt to stick to those words when consoling someone who lost their wanted pregnancy would come across as needlessly callous. . "I'm so sorry you lost that fetus, that's really tough experience for many formerly-pregnant people"
Context matters. It is a non-trivial issue when used in the context of terminating early pregnancy. Manipulating a teenager by telling her that she is a mother and she shouldn’t kill her baby is far more insidious than treating abortion as a women’s health issue, which it is.
The choice of words has a tremendous effect both on an individual and on the society. Ignoring this fact only leads to more misunderstandings.
If you were arguing that a pregnant person can identify as a father/father-to-be then you should probably have stated that.