They want to stifle the demand so as to match supply better, but when it's a supply shock and the United States is short something like 3 million houses, it seems a fairly punitive and misguided way to approach solving the problem.
Rates rising drives prices down. Of the mortgages on their books. And of the homes collateralizing them.
Add six people. There are now five chairs and ten people. How can you manipulate the prices of chairs such that all ten people can have their own chair?
Artificially lowering the prices of chairs does not solve the underlying issue: There are not enough chairs for everyone that needs one.
By treating housing price surges as excessive demand (raising mortgage rates), you lower demand not only for _existing_ homes, but also for creating new homes. If your goal is to ensure that housing prices always go up and affordability/homelessness go in wrong direction, the Federal Reserve's policy is very effective.
They're wrong to prematurely kill demand before it can cause new housing construction to increase, fixing the underlying issue of not enough supply.
Price always going up makes chairs attractive to hold, which results in misallocation of chairs - ideally you want them to go to whoever wants chairs the most, not whoever grabbed a chair first.
Yes, the best answer is to make more chairs, but that is not something that the FED has much control over (it's federal/state/local zoning policy and regulation which prevent more supply).
The question the FED can address is not "how can we make sure everyone has a chair", but rather "how do we make sure that the existing chairs go to the people that need chairs the most"
There's still a supply shortage in building homes to deal with, but that'd at least solve a problem for a good chunk of folks.
The solution is to remove tariffs on imported wood to make new housing cheaper and to punish municipalities with racial segregationist-era housing/zoning policies.
There are places like Mountain View that don't allow building above four stories, which is crap, but stuffing people into towering buildings where they're not allowed to own the thing they're living in or immediately priced out of it (which serves as an investment) doesn't solve the housing crisis.
Edit:
I had a bit of a snarky reply, and I apologize if you read that. I pay a little over $3.5k for a house (that allows a big dog); if I lose this place I'll pay over $4k in rent per month and that number goes up by the month. I'm being forced to come into an office, which requires me to live near by. If I can't live near by, then I have to accept a lower paying job. Do you see the complexity of this issue?
This is misguided politic theatrics, that causes even more panic and over consuming due to panic, which leads to further stress and supply issues.