To expand on this, it creates a bit of stratification of rents.  Existing rental units, limited by rent control, see potentially lower price, but new units aren't built in sufficient quantity, driving down supply.  What little does get built comes into the market at much higher prices.

So existing tenants get the benefit of lower prices but potentially worsening maintenance.  New tenants, or those forced to move for whatever reason, face much higher prices.

Landlords oppose them because it takes the decision making out of their hands.  It makes it much more difficult for them to adjust to market conditions.  It takes a long time (20+ years typically) to have a rental unit pay for itself.  It is always a risk to guess where demand will be over the next two plus decades, but with rent control that guess entails even more risk.