You're right, they do have a claimed reason for protesting that I didn't mention (rising rents), but I think it's a very poorly thought out one, based on emotion rather than rational thought.
If I was renting out a spare bedroom in my house to a college student for $500 a month, and then another guy shows up and says "I'll pay you $5,000 a month for that bedroom," what do you think my reaction would be? What do you think most people would do in that situation? I claim that nearly every one of the protesters, if they were in the position of the spare-bedroom landlord, would happily kick the first guy out and move in the $5,000 a month guy.
I can hardly imagine a way to satisfy the protesters' demands for cheaper rent without taking away that landlord's fundamental right to charge what he wants for use of his own property.
And by the way, tons of poor-ish and middle-class San Francisco home owners have made life-changing amounts of money from having their cheap homes increase in value when the tech industry moved in next door. But you never hear about them because they don't fit the narrative of the haves oppressing the have-nots.