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This is less a psy-op thing than it is a product of Western society's history - and I don't mean it as in "capitalism is bad and everything I don't like is caused by it", but literally living in such individualist society makes people live or want to live in smaller groups as much as they can afford it. And it dates before capitalist rise, in my opinion.
However... I don't think living in smaller groups, like living alone or with a +1, is inherently a bad thing. As people said here, there may be multiple reasons one would like to departure from their parents' house, a lot of them are genuine and to have this option is a good thing. What I see as a bad thing is that each house is meant to be a world by its own and in some places and contexts we don't have any community bond. This phenomenon contributes to anomie in Durkheim's sense, in my opinion.
One reason why I want to have a house to myself: organization. I live with a hoarder and a slob, which means the kitchen counters get filled with random stuff, and the floor has tripping hazards. Plus the generally unsightly nature of just having stuff jumbled about. While I am not a clean freak by any means (DUST!), I would like to properly shelf things or to walk around without surprises.
There are some things you can't really fight, one of them being wealthier relatives who own the shelter you reside in. So long as I am stuck in my current residence, I cannot have peace of mind beyond my room.