Yes, you are both correct. The problem lies in that each offspring is not identical to the parent, therefore it is a different organism, and thus can still be a parasite. The definition of "species" is a problem itself, because it's arbitrary.
You wont find a single reference in medical science that refers to a developing zygote or embryo fetus as being a parasite.
a) A parasite is an organism that, once it invades the definitive host, will usually remain with host for life (as long as it or the host survives).
b) A human embryo or fetus has a temporary association with the mother, remaining only a number of months in the uterus.