Since you, me, toddlers, teenagers, etc., have basic rights, and since there is no morally relevant difference (that is, relevant to whether one has basic rights) between us and human beings at earlier, prenatal developmental stages, it follows that unborn humans also have basic rights. This precludes killing them for the reasons that people have elective abortions ("unwantedness," convenience, economics, disability, etc.), just as our rights-bearing status precludes killing us for those same reasons.
The disputed premise is that there is no morally significant difference between unborn and already-born human beings. But consider the differences. Size doesn't matter, since big people are not more valuable than small people. Development doesn't matter, since a five-year-old girl is not less deserving of moral respect than her more-developed older brother. Location (in the womb or out) doesn't matter, since one doesn't become something or someone different by driving from Minneapolis to St. Paul. Dependency doesn't matter, since we may not kill breast-feeding newborns, parasitic uncles or people reliant on kidney machines or pacemakers. Intelligence doesn't matter, since smart people don't have more rights than dumb people. Appearance doesn't matter, since the "elephant man" was still, after all, a man. The sentiment of others doesn't matter, since a shunned and reclusive leper ought to be treated with dignity.
Philosophers who defend abortion offer more sophisticated criteria for excluding unborn human beings from the community of rights-bearing persons. But these differences don't matter morally either. The capacity to suffer doesn't matter, since people with congenital insensitivity to pain are still people. The possession of desires doesn't matter, since a Buddhist who succeeds in eliminating every desire retains his right to life. The capacity for self-awareness doesn't matter, since infants and temporarily comatose people should be respected and protected, not killed when we think it is in our best interest.
The strenuous intellectual efforts in recent decades to find some plausible exclusionary criterion have simply failed, as the recent work of philosophers like Francis Beckwith, Patrick Lee, Christopher Kaczor, Christopher Tollefsen and Robert George makes clear. Unless someone can find reason to think there is some actually relevant difference between unborn human beings and older, unquestionably-rights-bearing human beings, this "argument from no relevant difference" holds, and elective abortion is wrong.