Why do you say rent control reduces the incentive to build more housing?

To me it seems the opposite: Rent control means supply goes down, so available building & land prices go up. These prices going up means an opportunity for builders who are good businessmen because they are going to make a margin on their investment, the bigger the investment the bigger upside.

Another intuition is with rent control it's hard to extract new value from an old building, so that also incentivizes tearing it down and squeezing more units into the land.

In SF, rent control exists on all buildings built before 1979. It appears to me that people who prioritize new builds pay a huge premium for them. I think this particular rule also incentivizes tearing pre 1979 structures down, vs the no rent control newer buildings can continue to have growth in the value extracted from them.