Individuals do not necessarily exhibit fully rational behavior
To an individual, his own behavior is always rational. The concept of "rational behavior" is relativistic, making your absolutist claims absurd.
So, if I decide that what is better for me is to take away what you have
Firstly, that's not capitalism (as explained below), and secondly, that is not even what was being discussed. We were discussing what's good for each individual. As you point out, having resources forcibly taken is not good for one of the individuals, namely me; ergo, your example is pointless.
and once it's all gone, we're all fucked.
Clearly people will act out of self-interest to avoid that.
Capitalism just tries to take the things which are shared resources, and make sure someone gets to it first and claims ownership of it.
No, it's not. The question is indeed how to define ownership. Capitalism defines owernship as gaining control of a resource through voluntary interaction; all of your examples involve gaining resources through involuntary interaction, and therefore all of your examples are not of capitalism.