No amount of evidence will convince these people, because they already made up their mind ahead of time: their ideology says the market can't help, so the market can't help, period. Any evidence to the contrary is a plot by billionaires or something.
Maximizing supply can mean other things than building like taxing unoccupied homes by large amounts making them unpalatable to own as a second (or higher) home, thus putting them back on the market. However these aren't all good because obviously our economy deals with more effects than just simple supply and demand, like maximizing the amount of loans given to people wanting housing regardless of the ability to repay is known to be a bad idea.
If you throttle the supply you can clearly control the price and the people you're talking about believe there is a concerted effort to control that supply. This can happen directly (choosing not to build as soon as land is available to build on) or indirectly (e.g. politics, mass media influencing people to vote to not increase supply).
What people generally hate is production of essentials not being maximized which would give us the actual lowest price, and maybe we as a society should be maximizing that supply to arrive at the lowest cost for a given house with given features.
And then the rebuttal to that is usually "tough shit lol" which is why people coming out with simple supply and demand replies are generally seen as derisive.
It is of overall net benefit over the long term to raze a small three story walkup apartment and build something denser, overall increasing the amount of housing.
However, in the short term it's immediately quite (sometimes existentially) bad for affordability if existing affordable housing is destroyed and replaced by brand new (and thus inherently luxury) housing.
So accordingly we naturally see low income housing activists push back against some redevelopment and ask why development is not occurring in wealthy single family home areas where the amount of people impacted is less and class those that are not remarkably negatively impacted.
Personally I think the data shows that in general it is still really beneficial to build out as much housing as possible and avoid the negative impacts of a shortage, but I do think there are people validly pointing at a real problem of displacement.