why is this answer correct ?

I agree, can someone break this down please?

why not B?

Yes please, why not B

I'm just another test-taker here so please consider this with a grain of salt, but I rejected (B) because the conclusion of the argument doesn't actually "solve" the problem that "homelessness is a serious social problem." Instead, the conclusion seems to be dealing with a specific question regarding the larger homelessness problem: whether or not "further government spending to provide low–income housing" is an appropriate solution. The conclusion "people are homeless because of a lack of available housing is wrong" only addresses the specific proposal of increased government spending on low-income housing. In my reasoning, in order for the argument to try to "solve" the problem of homelessness, the conclusion would have needed to propose a solution, rather than solely rejecting a proposed solution.

isnt C saying that "homeless a serious problem" doesnt affect the conclusion. that the argument does not question whether homelessness is a serious problem.

The argument is not in fact trying to solve homelessness, rather the author is rejecting one approach to solve homelessness. The statement in question is just a fact, that is meant to introduce the politicians argument. Regardless of if you believe more government spending on low income housing is needed, one could agree that homelessness is bad.