Of course it's important to protect us. But this goes far beyond "offending" a group of people. Let's not forget that it was within the 20th century that hundreds of thousands of Japanese-Americans -- most of them US citizens -- were forcibly removed from their jobs and educational endeavors and relocated to internment camps, on the basis of the same argument you supply. "Offending"? How about violating constitutional rights? How about violating human rights? The constitution does not only apply to white people. Human rights do not only apply to white people.
In addition to being morally reprehensible, profiling is also quite useless. Although 99% of terrorists may be Arabs or Muslims, the percentage of Arab Muslims who are actually terrorists is quite small. Thus, profiling expends an astronomical effort on an enormous number of subjects to try to catch a very small number of actual terrorists. You have to search/interrogate/whatever a bajillion Arabs and Muslims to find that one terrorist. The yield is terrible, and you're much better off finding much more specific ways to target your search. The vast majority of bank robbers might own ski hats, but you do not prevent bank robberies by interrogating all those buying hats at Dick's Sporting Goods. It is important not to interpret a measure of sensitivity as a measure of predictive value.
Furthermore, once the terrorists are onto your profiling tactics, they can easily circumvent them. It's not that hard to make yourself look non-Arab, and/or to obtain a false identity, or for that matter to recruit a red-blooded American into your fold.
Defending against the present threat is a situation in which profiling just makes no damned sense.