Imagine that you're a young couple in a 1 BR apartment in SF that you're paying $1500/month controlled rent on. You wish to move to a 3 BR apartment, so that you can have enough room to start a family, and thereby free up the 1 BR apartment you're living in. Because you're married, and your career is starting to develop, your budget has increased to allow you to spend $2500, maybe $3000 on rent. Unfortunately, market rent costs much, much more than that, so you're stuck in your cheaper $1500 apartment, even though you can theoretically afford to pay more.

Rent control hurts affordable housing because it incentivizes over-consumption of affordable housing. Without rent control, average rents would rise, but it would be easier to find apartments at the low end of the market.