The city of SF is half as dense as Brooklyn and there are a lot of empty lots here. There is a lot more room for development. The problem is that the current political situation makes it easy for people to block new housing.This is quite an oversimplification, on multiple fronts.
For one, the reason Brooklyn has higher density has far more to do with historical building patterns than the current political situation, by any calculation for example. In Brooklyn, already by the 1930s, they built multistory housing throughout a much greater portion of available lots than they ever did in SF, for example. And then came the all the massive, federally subsidized housing projects in the 40s-70s (again, at a much greater scale than in SF).
The current political situation may not be helping much (from a growth perspective) -- but that's the just the current velocity you're talking about, not the starting point (i.e. the vastly greater stock of historical housing in Brooklyn over SF).
I showed up last Thursday and one city resident said we should not build housing [at the Baylands site] because an earthquake may cause the buildings to fall over.
Sounds like you're trying to paint this person as some kind of nervous nellie (or just another kneejerk NIMBYist). And yet it's easy to verify[1] that the lot you're referring to lies in a high-susceptibility liquefaction zone. So his concerns don't sound misplaced at all.
So again (and again, and again with these debates): Yes, NIMBYists exist, and the political situation isn't very particularly fun and often feels counterproductive, etc. But these aren't the root causes of the problem. Building (at scale) in mature, established cities is just, well, "complicated". And building in cities with a wealth of historic (and never, ever to be rebuilt) historic architecture -- which also just so happen to straddle one of the most dangerous fault lines on the planet -- even more so.
This really shouldn't be a surprise to anyone.
[1] http://gis.abag.ca.gov/website/Hazards/?hlyr=liqSusceptibili...