I don't really see that they hate our freedoms. I don't think they care at all about our freedoms if we keep them to ourselves. I really think it boils down to a religious issue. What they see as American/Western crusades into Muslim countries, Israel in Palistine, etc. I think if all Americans (well, I suppose all infidels really) left the Arabian peninsula and all Jews were exterminated and a Palestinian state were established, they'd be satisfied.
That ain't gonna happen, so therein lies the rub.