By San Francisco, I suspect they mean the San Francisco Bay area. While building in SF proper would decrease rents there, we can't have everyone who wants to move to the Bay Area live in San Francisco proper. Keeping this in mind, SF proper has a natural and inherent economic rent. So there is only so much pressure more building could relieve in SF proper. That said, I don't think many people would have much issue wi…
I'm not sure that's a given. Building lots of luxury housing in SF might actually decrease rent in Oakland and other parts of the Bay Area but not have an appreciable effect on rent in SF proper, at least in the short term. In fact, you could even argue that because of network effects and gentrification, building more luxury housing in SF would actually increase rents locally, even as it decreased rents regionally.
And that actually could explain why it's rational for some low-income residents of SF to oppose (or impose conditions on) new construction in SF itself. Increasing the geographic segregation between rich and poor can impact tax revenue, crime, education, transit, and regional politics in ways that particularly hurt the poor.