I don't know that we disagree as much as you might think.
I didn't say the police should be able to summarily arrest anyone who disagrees with them. But the fact is, if you misbehave sufficiently in the presence of a police officer, or if you challenge the officer's authority, you're likely to get arrested. Some places quicker than others, but I can't think of any jurisdiction in America where that's not the case.
If you know anything about the rest of the world, that's still a lot better than it is in most other countries. I don't know how much longer we'll be ahead of other places, but for now, for the most part, we still are.
Misbehave? Define please. He was upset. He had returned from a long trip to find his house broken into and finds the police were accusing him rather than looking for the perp. I might be pretty pissed too. Unless you can show me that he was violent, once Gates proved his identity (as he did) the cop should have simply walked away not put him in handcuffs!