Biologically speaking, a fetus is an organ till birth, given how the fetus' metabolism sync's ups to the mother's then rapidly accelerates upon birth, amongst other things.

Definitions of "parasite" include "An organism that lives on or in another organism of a different species" and "parasitism" as "an intimate association between organisms of two or more kinds especially: one in which a parasite obtains benefits from a host which it usually injures"

A human fetus/unborn baby is not a parasite.