It's a well-known observation among behaviorists and economists that people usually act based on their selfish interests, as opposed to the best interests of society. If you stand to benefit personally from rent control, you're much more likely to be in favor of it, regardless of its negative net consequences. This is especially true if you're not impacted by those negative consequences.

A recent turning point is that the number of adult renters in major U.S. population centers is beginning to exceed the number of homeowners. As they age, they begin to participate more in the political process (despite the voting age being 18) and carry more clout. You end up with two major blocs of political power: (1) city council members vested in the status quo who want to strictly regulate new housing to preserve "neighborhood character" (i.e., property values); and (2) renters demanding rent control.

Strange bedfellows they may seem, but the two kind of go hand in hand in the sense that they've already got a sweet deal and want to protect it.