If it is asked in an angsty-liberal-whiney "Why do they hate us" way, then it is a stupid question.
On the other hand it is a rational question to ask how they develop that much hatred and how can we short circuit that source. Is the hatred coming from Saudi-funded Wahabi mullahs? Then lean on the Saudis to really cut off funding and also work on becoming less dependent on Arab oil. Is the hatred caused by Syria whipping up an anti-American frenzy? Then support Assad's opposition and work to make sure he flees into exile or is hung in the public square in Damascus. Is the hatred caused by an uncontradicted series of lies from the Arab media? Then set up Radio (and Sattellite) Free Middle East to tell the truth.
Asking the question as a way to blame us is stupid. Asking it to find out the proper target for psychological warfare is smart.
On the other hand, it's a question that must be answered again and again, until people understand..
They hate us because we are "Dhimmi"..
We are "inferior" to them in their religious belief..
Yet, we do not submit, we do not bow down in humiliation..
We even out-do them in our accomplishments, and show pride, and independence, and self-confidence, even though we are not Muslims..
That is the ultimate insult to them..
The world has not bowed down to worship them as true believers and children of Allah..
Screw 'em..