The idea that rent control doesn't reduce available housing stock sounds true enough in the sense that people enjoying rent controls are less likely to move, and they count just as much as a new resident that might have displaced them, but from the perspective of the new resident the available supply is definitely suppressed and thus the price forced up for all non-rent-controlled apartments.
The other one is the unequivocal statement that long-term tenancy is better for the fabric of a neighborhood. In principal I agree with that, but I've known a lot of people in SF that would like to move but can't simply because they are priced out of the current market rate rentals. In these cases, it's not clear whether the benefit of having a controlled rent is worth the inability to move, especially if overall market rates could still be within reach sans rent control.