[E]veryone who is renting a house is renting it from someone who bought it, who is presumably not losing money on the deal. (Or is that a false presumption? Do landlords typically spend more to purchase and maintain their property than they make in rental income? How could that possibly be true?)

You can also ask a different question. If you borrow money to buy a house, you must find a lender willing to lend you at some interest rate. The interest rate is nothing but the price of renting money. So if it costs less to borrow (i.e. rent) the money to buy a house than to just rent the house directly, then how can the lender possibly be willing to lend you the money instead of investing it into a house himself and earning a rent higher than your interest?

When I make this argument, people usually try to argue that somehow you profit from buying by building equity with time. But if the money rent, i.e. interest, is equal to the house rent, then to build equity, you must make payments to the lender above this basic rent/interest rate -- otherwise you'll just keep renting the same amount of money indefinitely. And if you rent the house instead of making these higher payments, you can save and invest this difference, with the same positive effect on your net worth (which will also have an effect equivalent to the reduction in payments as the principal gets lower). Of course, this isn't true if the interest is lower than the rent, but then we get to the above question of why anyone would be so irrational as to lend at such terms. It also isn't true if the house price grows faster than any alternative investment -- but even ignoring the lessons from recent history, this again gets us to the question why someone would ever lend you the money at this cheap interest rate instead of investing the money himself into these fast-appreciating houses.

What these considerations show is that according to the textbook spherical-cow microeconomics, on a free market for housing, renting and buying should be equally good deals, since in efficient markets there is no possibility of arbitrage. And buying can be profitable over renting only if there is a strange opportunity for arbitrage where it's cheap to rent money but expensive to rent a house, even though money and houses are readily convertible into each other. A similar argument can of course be made against the possible advantage of renting -- except for the issues of risk-aversion and asset diversification, which decisively favor renting over owning.

In reality, of course, these simple spherical-cow models don't work, and there are lots of complicated and ill-understood factors involved, including all sorts of people's biases and signaling issues, high transaction costs, Knightian uncertainties, exuberant speculation, and not the least of all, huge government interference in the market by various subsidies, regulations, and other convoluted and dubious enterprises. The result is a complicated mess in which an accurate analysis of what's really going on is practically impossible, and in which there may indeed be possibilities for arbitrage.

However, regardless of all that, it seems to me that buying has some tremendous drawbacks, for which I can't see comparable upsides under any realistic circumstances. The first and foremost is that you're investing the bulk of your net worth (and on top of that a huge pile of borrowed money) into a single non-diversified asset, which seems like a crazy idea by the most basic principles of sound personal finance. [1] For various other drawbacks, one could perhaps argue that they are offset by the downsides of renting (though I would disagree), but this one really seems to me by itself like a decisive argument against getting into house ownership.

[1] Note that this is one possible solution to your landlord puzzle. The tenant may want to pay a premium to avoid placing most of his net worth into this asset because of risk-aversion, while for the (rich or corporate) landlord, it's just another item in a large portfolio with the risk well spread.