The reason is that landlords know exactly what rent control does.
Landlords know that the tenants with the strongest interest in local housing costs are the people who already live there and plan to continue to do so indefinitely. Rent control is a method of buying them off without actually solving the problem in general, so that overall rents and housing costs remain high but the subset of people most likely to be politically active in doing something to correct that gets a bribe to stop objecting while overall housing costs continue to rise faster than inflation.
What it is, then, is not a step on the road to a real solution, it's a roadblock preventing that from happening by weakening opposition to the status quo by just enough that no actually effective reforms can be enacted.
It's the sort of false compromise that happens in politics all the time. Instead of solving the problem, you enact some alleged solution that really does nothing or makes the problem worse, but then politicians get to go tell the voters that they've done something. Then, when it doesn't work, they get to go back and pass another ineffective bill to "solve" it again in the next election cycle, meanwhile we get another four years of young people not being able to afford housing.
If you're asking how to get that passed, well, that's an education problem. You need people to understand why rent control is not a solution so that they are not willing to accept it over something that actually works.
