Their core argument is that we could increase supply but choose not to, and that we should be maximizing supply (as an ethical and moral mandate, but that is not a tenant of capitalism really) because housing is an essential thing like food and water. FWIW we don't maximize food/water production either for various reasons, which would also drive food/water prices down.

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.