Concerning the "potential" argument: if you argue that a fetus should come to term because it could become the person that cures cancer you have to consider the opposite is just as likely. An abortion could kill the next Hitler. The fact is we don't know and we couldn't possibly know unless we debunk philosophical concepts like free will. No one has a particular destiny-their path is the result of choices they make and they could wind up taking any number of paths before it's said and done.
Second, it makes no rational sense to limit this argument to human beings. We like us, sure, but I'll bet there are plenty of creatures that think they'd be better off without us, and many of them would be right. In eating a certain animal or breathing a particular spore, you may be destroying a form of life which, left alone, would evolve beyond us in a few billion years and accomplish things we could never dream of. Likewise, by perpetuating our existence we may be damning the planet. It's not set in stone; in fact we could turn out to be the best thing that ever happened to earth when it's over, but that's just it. We don't know. It's predicated on things we haven't done yet.
There is no rational, objective argument against abortion. Regarding when life really begins, that's largely a philosophical construct and it's not something set in stone. We may be able to create a better informed standard once we have more knowledge of the human brain but it will still be arbitrary if it's before the point that the child-to-be can maintain an independent existence from its mother. Pro-life arguments have an emotional resonance but what I have seen has no content beyond that. (Though again I want to stress that I respect pro-lifers who can make thoughtful arguments.)
From a purely emotional standpoint, I can accept the things that come with abortion more easily than I can accept what happens without it. Forget when life begins, if a kid is going to be born into a household where he's not wanted or he'll be stuck in poverty and die young from a lack of healthcare then I'd rather see the mother terminate the pregnancy. As I said earlier, we can't care for the people we already have, and the fact that pro-life usually means "against social programs" as well it's an indefensible stance. I feel for pro-lifers who don't fall in line with all the right-wing rhetoric but what they want isn't feasible in a world with limited resources that already has an overpopulation problem.
In short: you want a world without abortion? Work to make it the least attractive option. That means improving the quality of medical care and increasing its availability, it means creating systems that better serve the parentless children in this world, it means eliminating poverty, it means improving educational methods and standards, and lots of other things. If people want to argue the politics of it fine, just remember that while they're doing that a whole bunch of worthwhile causes are being ignored for the sake of people who don't exist yet and who are much more probable to be born into horrible circumstances if pro-lifers succeed.