To most Moslems it’s perfectly natural to hate Jews and insist that Israel should not exist. These are indeed alien concepts to most Westerners and non-Moslems. To get a better idea of where Moslems are coming from consider the fact (based on opinion surveys of Moslems) that most Moslems see themselves as Moslems first, and feel that the non-Moslem world is out to get them.
The intense hatred of Israel is better understood if you keep in mind some key elements of Islamic history. First, Islam is a very intolerant religion. Their scripture calls for any Moslem who converts to another religion be killed.