I don't know, maybe they prefer to live on benefits in a cheaper place? If you live on government support, jobs in your area don't help you and the higher prices worsen your situation.
Ultimately, they call that place their home and wish to say. Market economics however are forcing them to move. Therefore, conflict exists.
Honestly, the solution is to build more Apartment complexes and strike down the zoning laws that prevents the new buildings from going up.
(You can make maps like this at http://propertymap.sfplanning.org/)
It is strange to see Anarchists as the ones who are most rebellious against gentrification.
However, the housing market in SanFran is anything but free.