Actually, having had my head in immune system lit all day, there's actually solid immunological arguments for the fertilized egg being classified as a parasite, and most immunology journals openly refer to blastulas/zygotes/etc as such. The way a blastula overrides the maternal immune system to hijack her arterial blood supply is actually exactly how parasitic nematodes do the same- via a phosphorylcholine sugar-protein that destroys the major antigen receptor in host/maternal cells such that she isn't able to recognize the foreign body.
Super cool, kind of makes you wonder how there aren't more diseases that take advantage of the number of Achilles heels in the human immune system. Though there's certainly quite a few already. I kind of got sidetracked on the germ theory of autoimmune diseases (hygiene hypothesis) and didn't read further. But maybe that's why Ridley Scott made his Alien look like a giant vicious moving placenta (the similarity is undeniable! That skin tone and texture!)
General biology books refer to parasitism as involving two separate species, and the species concept is kind fallacious too. Most biology faculty won't even admit to supporting the biological species concept, because it falls apart in light of the fossil record, microbiological life, and you just start to realize everything is arbitrary and usually incorrect taxonomy- superimposed systems of organization that have nothing to do with the spectrum that life and time is.
All I know is that I'll never forget when I walked in to my third grade classroom on a Wednesday and saw the carnage of our class pet- a pregnant hamster- having eaten two of its newborns. Oxidized blood all over the overpriced hamster cage bedding.
What is and isn't human is irrelevant. Termination of pregnancies by the mother is going to happen whether it's socially and legally supported or not. You just have to ask whether or not you want to live in a society that does it behind closed and unsafe doors, or provides clean safe medical care.
In Ireland, where I grew up, there's a huge online black market for RU186 and a trip to England will run you about a thousand euro. I haven't looked into America. I'll spare the more coat-hanger intensive processes I've learned of from all my Aunts in the medical field.
Biological delineations are arbitrary and superimposed. Even if they weren't, motherhood is mostly just endocrinology and not very rational at all. I personally don't want to live in a society where 14 year old girls fuck up once, or are fucked once, and have to go to Dante's Inferno to recover. There's a reason Silphium was hunted to extinction in Rome.
TL/DR: Biological definitions are usually arbitrary and always irrelevant in the face of what's actually implementable. Searching for political labels is a waste of time and usually an excuse to not take the time to understand.