If Europeans had already developed the idea of private property, then why did we find it necessary to take the land of these ingenious populations?
Ok, so that's more "how" than "why". The "why" was because they wanted it.
You can't say, "I claim this piece of land for my own. Oh, look! There are people living on it already. I guess I get to enslave, rape, torture them." This has more to do with brutal people being the first people to encounter the natives in the Americas, and deciding that since there was no European justice system or society to condemn/jail then that they could do whatever they felt like.
Actually, you can say EXACTLY that. The very idea of private property is founded on that principle. When whoever it was originally decided some plot of land belonged to him, that's precisely what he said. All I would add to that statement is the clause, "Or they can get the hell out."