Correct me if I'm wrong here, but I don't think they "just moved in". They've lived there for a long time as well, but the former country of Palestine was quite divided ethnically, and that caused issues due to extremists (on both sides).

The purpose of splitting Palestine was to get two countries that were at least less divided ethnically, but due to where people lived Israel still remained quite evenly divided between muslims and jews whereas the new Palestine was close to 100% muslims.

Countries have been split all over the world before in somewhat similar manners without causing as big conflicts, showing that this could've been done in a peaceful manner. What went wrong here? I don't know.