I don't think "they hate us for our freedoms." I think they might hate us for other reasons, though.
If an army came to Los Angeles, where I live, and bombed the living shit out of it, I might be upset. If that army destroyed my city because they were looking for WMDs that didn't exist, WMDs which the army's commander in chief KNEW didn't exist, I'd be deeply upset and angry. If that army tortured my fellow Angelinos, most of whom knew nothing about any insurgency movement that had sprung up against said invading army, I would be outraged. If soldiers in that army did a search of my house and interrogated me, and stood over my shirtless son holding AK-47s, my six-year old son, a CHILD, I would be enraged.
I might even hate. I might be filled with hatred for that soldier.
But if I had time to talk to the soldier, one human being to another human being, I might realize that he was just following the orders of a horrible man, a man who had lied to him. A horrible man who sent the soldier around the world to see and do horrible things.
Given time to talk to the soldier, I might realize that that soldier joined the army because he was poor and needed work to provide for his family. Or that he was ignorant and unschooled. Or that he simply trusted the word of his lying boss. I might see that the soldier wasn't really free at all.
And I might have a chance, if we really talked, to ask him to tell his boss, "I don't hate you for any reason other than that you are in my country, destroying my home, and terrorizing my family. Wouldn't you hate someone who did that to you?"