Crowley did act like the bigger man. He gave Gates his information, confirmed there was no crime in progress, radioed pertinent information back to the dispatcher, and made ready to exit the premises. Crowley acted, by all available evidence, like a solid professional.
Crowley did not bring Gates outside. Gates followed Crowley outside so he could shout racist garbage at him. Gates picked a fight with a cop who did his job and was in the process of leaving. Gates intentionally escalated that which did not need to be escalated.
Crowley did act like the bigger man. Unfortunately, Gates decided to play the very small man and would not let Crowley leave without a fight.
When you fight in public, it's called disturbing the peace, and you go to jail while you cool your hot head down. That's what happened. The hahvahd nobody picked a fight, went to jail for his time out--which is the correct thing to do when someone is acting like a spoiled brat. No racism, no abuse of power, no impropriety.