Perhaps the Professor "lost his cool"; however, if I was in my own home and the police showed up to arrest me for breaking into it, I'm not sure how calm I would be, either.
The cop did not show up to arrest him. A call was made that two men were trying to open a door with their shoulders (we now know that it was jammed). In properly checking on the situation, the cop asked him for an ID to prove that he lived there and Gates flipped out, exposing his own racial hostilities. Perhaps he should have been a little more grateful how quickly the police came to investigate a break-in at his house.
