makes perfect sense to me, if they found a one celled anything on Mars the news would scream "Life found on Mars", but the baby has to be called fetus which in their mind is merely an inconvenient clump of cells and bothersome tissue.
Nope. Actually, the child, regardless of stage of development, is not "part of the mom." He/she relies on the mother for a lot on nutrition and nourishment for development, but he/she is still a separate being.
People are not created by parthenogenesis or budding.
Human reproduction creates a separate life form which is separate. Look at the function of the placenta for proof. Mothers blood never mixes with the babies blood.
parthenogenesis and budding are methods in which another creature/plant is created from an original - they are literally part of their mother. Humans are not part of their mother, they develop inside of their mother and are separate entities when sperm and egg combine. The placenta is the key here, it is the interface between mother and child, protecting the child - even from the mother.