It seems so simple. Even logical. Who doesn’t agree that we need to encourage and enable a way for middle-income families to live in the San Francisco?

You know the story. With this hot housing market, schoolteachers, firefighters and police officers are being forced to move away by high prices. If only there were a plan to create moderate income housing for them in the city. Oh, and it would also be nice if it could be done without using city funds.

And there is. Mayor Ed Lee’s affordable housing density bonus plan — and congratulations on winning this year’s clunkiest program name — would create thousands of below-market housing units for middle-income residents. No city money would be used, because housing developers would get some considerations, like an extra two stories of height, if they make 30 percent of their projects below market-rate. Eighteen percent of those units — as many as 5,000 over 20 years — would be for moderate- and middle-income residents.

Who wouldn’t support that?

Lots of people. You’d expect complaints from the pull-up-the-drawbridge crowd, who regard any building in their neighborhood as a betrayal. But the surprise here is the stiff opposition from advocates for low-income housing.

The plan has been tweaked a bit with the hope that the Board of Supervisors will approve the idea. But so far supporters feel the opposition has the six votes needed to turn it down.

“It’s strange,” says Supervisor Katy Tang, a co-sponsor of the mayor’s plan, “because the champions of affordable housing seem to be the ones opposed.”

And it isn’t just respectful disagreement. Voices have been raised, Planning Commission meetings have dragged on for hours, and hyperbole reigns. At a contentious meeting in the Sunset, residents fretted over Miami Beach-style towers along the ocean. One woman claimed it was all a plot to evict rent-controlled residents in the Mission and ship them to her neighborhood.

“We think this will benefit a lot of people who don’t come down to City Hall,” said Jeff Buckley, the mayor’s housing liaison. “But the vitriol has surprised us.”

There’s a nasty undercurrent to this. It is the idea that low-income folks deserve help while middle-income types are a bunch of entitled young jerks who already have enough going for them.

That doesn’t play well on any level. Of course neighborhoods should include mixed incomes. And that means every neighborhood and every income.

“The city has no tools to address families of middle income,” Tang said. “This is a tool to address that.”

And yet, conspiracy theories persist. For example:

This is a ploy to evict rent-controlled apartment dwellers: Actually it isn’t. In January, Board of Supervisors president London Breed drafted an amendment that specifically says no rent-controlled unit would be demolished. Even if there were only one rent-controlled unit on a parcel, the entire parcel would not qualify for the program.

And, yet, I am still getting emails from people who believe this would happen.

“I think I’ve given up on it,” Tang said. “I’m so frustrated. We are not going to demolish rent-control units.”

This is a premise to build tall, view-blocking towers: Nope. If developers provide 30 percent affordable housing (12 percent low income, 18 percent middle and moderate) they would be allowed to add two stories to a building.

For most builders, adding the extra two stories makes a project work financially, and the affordable housing benefits the city. But six stories is hardly a tower.

Still, demolishing existing structures hurts the character of the neighborhood: A case can probably be made for that on some level, but the plan is to start with “soft sites,” which are vacant lots, abandoned single-story buildings and parking lots. The Planning Department has identified 240 soft sites throughout the city, which it says could add 16,000 housing units, 5,000 of which would be affordable.

Small businesses will be the real losers: That’s a legitimate point of contention that needs to be addressed. Commercial units are not eligible for rent control, so they could be targeted by housing developers. Tang says the Small Business Commission has made some suggestions, including requiring a commercial space on the ground floor, limiting the square footage to discourage big chain retail and giving the current business first right of refusal.

“If anything, that should be the focus” of critics, Tang said, “rather than possible towers.”

The city is forcing this on residents. If we just leave things alone, everything will be fine: Sorry, but no. A state affordable housing law has been on the books since 1979. It is a lower standard than the mayor’s plan — only 5 to 20 percent affordable housing required per development project compared to 30 percent for Lee’s program — but it is settled law.

C.W. Nevius is a San Francisco Chronicle columnist. His columns appear Tuesday, Thursday and Saturday. Email: cwnevius@sfchronicle.com Twitter: @cwnevius