[povik]

> It seems to me this is simply a statement that an electron is a fermion not a boson, right?

Not really, that's a property of any quantum particle, bosons also. They don't occupy a single point in space like you would imagine classical particles do. They also cannot occupy a single point in space relative to another particle.

> It's a fermion, but why should it be?

Well there's the spin-statistics theorem in quantum field theory which starts from some likely assumptions and then shows that particles with non-integral spin must be fermions while particles with integral spin must be bosons. Other than that I take it simply as an experimental fact. I don't think there's a nice reason for it one could give (today, that is).