I personally wish President Obama hadn’t directly criticized the lamentable arrest of Harvard scholar Henry Louis Gates Jr. by Cambridge police on Tuesday. Obama made two factual errors in his remarks — Gates had not forgotten his keys, they didn’t work because his lock had been broken in a burglary attempt; and he didn’t jimmy the door open, he got in the back door — which suggested his comments weren’t fully informed, as correct as his ultimate judgment may turn out to be. I understand and support his desire to speak out against racial profiling; I wish (and I’m sure he does too) he could take back the statement that the police acted “stupidly.”

I myself am not sure if the Cambridge police acted “stupidly” in arresting Gates; we don’t yet know all the facts, although from what we do know, it seems an arrest could have and should have been avoided. But I will say conclusively that they acted stupidly on Friday, holding a blustering press conference to support Sgt. James Crowley, the arresting officer, but then saying Crowley wouldn’t speak. Of course, Crowley has been speaking, selectively, to the media, so it was a strange decision to mute him today — especially because he’s come across as fairly sympathetic when he has spoken up. An even stranger decision by the local cops: To announce the support of multicultural police associations, and to assemble a diverse roster of male and female officers behind the podium – but then, to only choose to have white male cops speak. Not smart. Not smart at all. Downright stupid.

I think between them, James Hannaham and the Ivy League African-American who chose the byline “The Phantom Negro,” have summed up all the complexity of this case, and its basic simplicity, too. There’s almost no compelling reason for a man who walks with a cane to be arrested in or just outside of (there’s some debate about which) his own home, whether or not he mouthed off a bit to the cops. There’s also no compelling reason for Gates to have mouthed off the way he did, if Crowley’s account is to be believed, since at least in the origins of the police visit, they were trying to protect Gates’ property, not harm him.

And while almost no one is talking about it, class is nearly as relevant here as race. There is often tension between working-class cops and academics, whether students or professors, in campus towns. The assumption by the liberal elite, from President Obama and Gov. Deval Patrick on down, that the well-off, well-loved, well-connected Gates (defended by his best friend in the Washington Post though the piece is only online in Gates’ own TheRoot.com; interviewed, unbelievably, by his own daughter for the Daily Beast) was completely in the right here, has to gall these white working-class cops.