Progressives believe that allowing developers to build housing will only create "luxury" housing that is unaffordable to all but the rich, increasing gentrification and displacement. Therefore it's necessary to mandate things like "inclusionary zoning" and tight review of every single development project.
Empirically, the progressive stance results in a lot less housing of any sort getting built, whether "affordable" or otherwise, and consequently higher housing prices for all but the lucky lottery winners who grab the limited number of BMR ("Below Market Rent") units. Some would say that that's actually the goal of progressives (ie, they're using "progressive" window dressing to preserve property values/neighborhood aesthetics of the very rich).
20 years ago, progs would admit outright that they thought new development was undesirable. Since, it has become more inappropriate to say that out loud so they dress it in concerns about only supporting housing under economically infeasible conditions.