First off there is a big difference between birth control and sterilization. Birth control helps us manage pregnancies and bring children into the world in more favorable conditions. Humans actualy benefit from using birth control.
In my opinion it is wrong for a person to purposely sterilize themselves before procreation. If we all sterilized ourselves before we made children the human race would cease to exist.
There is nothing wrong with the structure of the argument. Things that hinder the success of the human race are inherently wrong.
Once again, it's about the structure of the argument. The point is that many things which are "good" or neutral in one context would be "bad" if everyone did them. We don't have to even restrict it to reproduction. Fundamentally, that is a bad way to argue, since it doesn't tell us anything about the inherent qualities of anything.
As for "success," that's a very loaded term, and certainly not a scientific one. The idea that the "purpose" of life is to reproduce is not a scientific one when you make it a moral imperative. What scientists mean when they say that (and frankly, it's misleading language, so it's partially their fault) is that it's a strong general tendency that exists within living beings. It's an empirical descriptor of something that happens, not a moral guideline or the basis for morality- something that should happen. So in short, the idea that we should base morals on what hinders the human race can only be subjective, and thus requires consensus, not an objective basis, and furthermore is dangerous insofar as it ends up in potential tyranny.