If you're from the U.S. you seem to be forgetting some very hard lessons that were paid with blood in the past. There is a reason why we have a bill of rights. There is a reason for our rule of law, of requiring warrants before searches. That our 'forefathers' said that it's better that 10 guilty men go free than one innocent man be falsely charged. Racial profiling is wrong because you're infringing on the freedoms of innocent people that have committed no crimes.

"Aren't you just making statistical inference based on past experience?"

Yes, but if your behavior in the past was also biased, going off of arrest records or something like that won't get you better / less biased results.

Racial profiling works to some degree, but it means that innocent people who match the profile have to put up with a lot more intrusion into their lives. It's similar to the moral question about where to draw the line: would you rather imprison an innocent, or let a guilty person go free?