SF does have a much bigger homeless problem than other cities, and whether it is cause or effect, it's at least correlated with significant and chronic drug use.
I live in an area affectionately known as the 'tender knob'. We've had people defecate on our steps, tear open our garbage bins and leave litter everywhere, and shoot up drugs and leave dirty needles in our outside stairwell. Before moving to SF from NY, I had never seen people defecate on the middle of the sidewalk in the afternoon. The owners of our duplex live upstairs and they've been brought to tears having to deal with this on a weekly basis. I wouldn't feel safe having children in this area.
Yes there are homeless people who had some bad luck and are just trying to get back on their feet. Most people are sympathetic to that. But it's different in SF. Walking around you can't help but feel that many, if not most, of the people are chronically homeless drug addicts who have passed the point of no return. That's the problem we need to deal with.
Moreover, there seem to be strong network effects at work here. You might argue that by not 'pushing out the homeless', that you're actually maintaining a dangerous, self-reinforcing, social environment that is constantly attracting new members. In effect, are we making the problem far worse?