Well,
first off what kind of profiling are you talking about? Racial/ethnic profiling, religious profiling, forensic profiling, offender profiling, etc. There's a lot of different kinds. I'm assuming you're discussing racial profiling, please correct me if I'm wrong.
Secondly, the biggest question is, does it actually work? I've read a couple different studies, but the general consensus seems to be that yes, it is effective to a degree, at least for certain crimes. One of those studies is linked below.
Racial Profiling Works!!!: Operations & Tactics at Officer.com
Finally, you have to consider the fact that it creates a very adversarial relationship between members of the groups being profiled against and the police/TSA/whoever. It also subjects a lot of innocent people to major disruptions in their travel plans for no other reason than they're members of a certain race, which is (perhaps arguably) against the 4th and 14th amendments.
Taking all that together, personally, I don't believe the benefits of profiling are worth the downsides it carries with it. If it were more effective, I might feel differently, but profiling isn't a magic bullet against terrorism, it's just one tool among many.