A parasite is defined as any creature that is biologically dependent on another organism for life and offers no tangible benefit in exchange for its being kept alive. On the contrary, parasites are typically harmful to their hosts' bodies. That is a fetus, to a T. The harms of pregnancy range from vomiting and seasickness, to night terrors, to weight gain, to changes in appetite and libido, to scaring, to bladder incontinence, and so forth. (Not counting, of course, the delights of childbirth.)
The fetus gets nutrients and oxygen from the mother and provides nothing useful in return. This, by definition, makes it a parasite; An organism living in or on another in a way that harms or is of no advantage to the host. Despite the fact that the fetus is the host's child, it provides no physical gain to the host. This does not mean they provide a serious threat to the health of the mother.
The emotional bonds and attachments aside, fetuses draw their subsistence from the mother and provide no biological benefits in return, which does, strictly speaking, make them parasites. Though, the term 'parasite' carries an inherently negative connotation. Fetuses would be one example of the flaw in this thinking; they are a parasite which is not usually harmful.
A parasitic relationship is where one organism benefits while the other suffers. That is not the case when having a child, since the emotional attachments prevent you from suffering. Actually, in the fetus stage, its more of an indifferent relationship, since the fetus benefits, but the mother doesn't suffer nor get anything out of it.
I think of parasites as something that is truly separate from the host and either unwanted or evolved into the relationship. Any species has a reproduction process that somehow involves life passing from one unit to another, and that is all that occurs when a fetus is living inside of a mother.
Typically a parasitic relationship is non-mutual and negatively affects the health of the host, often resulting in death. The fetal/mother relationship is much more mutual. The fetus does take up extra energy from its mother, but the mother passes on her genes through the fetus, making the relationship mutually beneficial.
Fetuses are in no way a 'parasite'. They are the same species as their mother. They obtain nutrients and oxygen from their mother thru the umbilical cord. Life starts at conception and continues in the womb for nine months, then it is out into the real world. Human babies are dependent on their parents for care much longer than other species of living creatures.