This is the part that, unfortunately, many people don't realize. Islam from its very beginning was developed as a justification for military conquest, and this is inseperable from the religion itself.
By the way, there are plenty of moderate Muslims, but only because they're nominal Muslims who don't really hold to the foundations of their religion. So you were correct in the first place. There may be Muslims who call themselves moderates, and moderates who call themselves Muslims, but these tenets are in reality mutually exclusive.
Of course, judging by how many times Israel has kicked Arab butt, they haven't been doing a very good job of it lately.