The analogy between fetus and parasite fails on a couple of important counts. A fetus, unlike a tapeworm, is not an organism of one species living in another. Fetus and mother, I dare point out, are of the same species. A fetus, unlike a parasite, does not die once separated by birth from the "host organism." It thrives and continues in a positive and healthful relationship with the mother.
At least, the claim wasn't made that a fetus is a cancerous tumor or evil spirit that must be exorcised.
I'll leave biologists to fight over what appears to be an essentially linguistic argument of whether fetus is a subset of parasite. As for laymen, most still will recoil at the thought that a developing human is akin to a scabies mite, blood fluke or Wuchereria bancrofti, which can lead to elephantiasis.
The mind rebels at the thought because the human mind innately knows that the "thing" in the womb is one of us.
That anyone could consciously reject that knowledge is frightening.