Actually, if a new person is defined as occurring at the moment of conception. then the right to self-defense from this human also should begin there (speaking of how the law would read if it were consistent, at lest to me). You can't claim self-defense from a blob of tissue, but you can from a person.
And this is where the debates start, as in what obligations do the mother have to the child, what rights do the child have in regards to being born, being protected, is the child viewed as an attacker or as a victim, after all it didn't ask to be created, so it didn't force its way in, it happened as a result of actions far far beyond its control, as perhaps it was with the mother as well, does the constitution protect each equally, if the mother has a right to self-defense against the fetus does the fetus have the right of self-defense against being aborted, whereas it cannot realistically defend itself so do we have an obligation to defend it as we would a person who is of diminished capacity, or, in fact, a child that has already been born, and if the mother succeeds in defending herself against it, is it a crime, since the fetus had no capacity to defend itself, does the fetus at that point, being deemed human life, have a right to be born at all, etc. etc. Anyone can put forth their opinions on these questions, and use whatever logic they choose, but it still remains opinion.
These philosophical debates are virtually endless and realistically unsolvable. Science cannot provide answers to any of these questions, aside from the approximate point of viability outside the womb, and opinions will vary wildly, and for different reasons and motivations, and none any more valid than any others, excepting of course the wildly illogical ones.
And in the end it boils down to who should get to choose what happens in this situation. To me the answer is that it needs to be the mother, even if I disagree with any or all of the other arguments. I certainly cannot choose. "Science" cannot choose. The government certainly cannot choose. At least none of them know any better than the mother does in the circumstances. So regardless of my, or anyone's, feelings on the matter, realistically that choice, and all of its consequences, need to be left to the mother, or her guardian or caretaker if she is very young or incapacitated, but certainly not the courts nor the general populace nor the government. They don't know the answers any better than anyone else.
To be certain it is a complicated and emotionally-driven matter.