It's not an aversion to property rights in general. In particular, it isn't an aversion to allowing private ownership of the means of production (communism) or, on the flip side of the modern acceptability coin, private ownership of people (slavery).

You're right that the phrasing of the argument was general. There are more specific moral arguments on every side of every one of these, but the practical side of it always boils down to: how do you preserve incentives in a market's growth phase while discouraging rents (in the economic sense of the word) in the steady state?

That's a tricky one, and I don't claim to have a general answer, but I'm pretty sure that in the particular case of land it has something to do with society not making unbounded promises in exchange for bounded goods, e.g. of eternal, transferable land exclusivity to a private entity in exchange for building a log cabin on it. From that perspective, the government of past generations stole the exclusivity rights from modern citizens, and the present landowners are in a situation similar to any other possessor of stolen goods.