And yet, per the video cited by the OP, the distinction between "potential human" and "human" is immaterial. We can debate where human life begins all day, but from a human rights perspective it actually doesn't matter whether a developing unborn baby is a human yet or not. If the rights of the mother are to be at all considered, we should ask whether humans have the right to remove themselves from biologically and financially parasitic relationships with other humans. Should the government have the power to force people to stay in such relationships?
From a purely moral perspective, I believe that the 98.5% of abortions committed for convenience reasons are without question immoral. Scientifically we know that a new human being comes into existence at fertilization, and I personally believe that all human beings are morally valuable and possess the same inherent moral worth and value.
We all take about 25 years to fully develop, yet at no point during our development are we not a human being or less inherently morally valuable.
But I agree that the law isn't really in the business of regulating morality. Alcohol I think is a good example. As a Christian, I believe that alcoholism, and getting drunk is immoral and wrong. However, I don't think it should be illegal to get drunk.
I do agree with laws such as no drinking and driving. Why? Well, the purpose of no drinking and driving is to protect innocent people. On the one hand, it protects the drunkard who is too intoxicated to think rationally not to drive. It also protects the people he may encounter on the street.
Our laws really should be focused on protecting people. That's why there are speed limits, they are meant to protect people from other people who would drive wrecklessly (see what I did there?!).
As a good American, I'm all about the right to life, liberty, and the pursuit of happiness. Yet, we all agree that all of those "rights" may be temporarily suspended, or permanently revoked. It just depends on the situation. If I'm a kleptomaniac and my pursuit of happiness involves indiscriminately stealing from stores, well then I'm out of luck because I don't have the right to pursue that type of happiness because it harms others.
Every single person in jail has had their right to liberty temporarily suspended. Every single person on death row, or in prison for life has essentially had their right to life removed.
We all agree that there are times in which our rights are suspended.
Applying that to abortion - I would argue that the unborn are the most innocent and vulnerable of us all. They have done no wrong, and they should be protected. I believe this because I believe that all human beings are inherently morally valuable. Therefore, I do think the law should protect the unborn, because the unborn are just as morally valuable as I am.
Now, if I didn't think the unborn were as morally valuable as I was, I probably wouldn't have a problem with abortion. Thus, at the end of the day, I think the abortion debate really centers upon how we consider the nature of the life of the unborn. Are they human beings that are inherently morally valuable? Are any of us inherently morally valuable? If not, then abortion is fine. But my foundation of inherent moral worth and value to all human beings logically and necessarily results in the conclusion that at the very least aborting health growing babies is morally wrong, and would therefore be a form of murder - which the government should protect against.