The “profiling” that Obama is trying to imply is based on race, not an article of clothing. An article of clothing is a voluntary decision that usually expresses something about you and which you have chosen to wear to make that statement, show your membership in some group, etc.
My son - who is 100% white - never had any problems with the police as a teenager in a small CA city - until he started wearing a type of leather jacket that was very popular with thuggish white kids at the time. It was also popular with heavy metal singers, and he was wearing it because he was going through teenage music-that-drives-your-parents-mad stage. He was not a criminal or associated with any gang.
However, one evening he ended up being forced to lie spread eagled on the ground by a highway while the highway patrol pointed a gun at his head - because they had been on the lookout for someone wearing that type of jacket who had robbed a convenience store. Fortunately, they found that the city police has already caught the other guy, so they dusted him off and let him go. He dropped the jacket from his outfit soon afterwards...
The “hoodie” is associated with a certain type of behavior, and whether or not you actually engage in such behavior, people will be a little worried about you until you prove by your actions that you are simply wearing it to keep warm or for whatever non-crime related reason.
This is a normal human reaction and has has nothing to do with race. Visual signs are what allows any animal to detect danger, and the hooded sweatshirt has become one of those signs.
Incidentally, our white thugs here in Florida often wear them, probably because it makes it easier for the to hide their faces while they are committing a crime.
For some reason, the popularity of hoodies seems to follow the advent of security cameras.