What is wrong with profiling of people for criminal activity?

Profiling of people based on behaviors and some other attributes should be used when looking for criminal activity. A person traveling alone on an airplane without luggage on a one-way flight should be suspected and given a more thorough security inspection than an elderly couple with a round trip ticket. A person who can not speak English would be more likely to be an illegal immigrant than someone who is fluent. A person dressed like a hoodlum flashing gang signals in an upper class neighborhood looks out of place and should be investigated. The same with a well dressed person with a luxury vehicle in the ghetto. So why are people so against profiling that we end up treating everyone as criminals?