This is a bit of a fallacy. In a normal market, the rent for a home is less than the costs of home ownership (mortgage + maintenance + taxes) and that saved money can be used to purchase other assets.

Until the real estate mania of the last few years, if you followed this strategy, you would not be any worse off than the person who bought their home.

I personally would much rather have equity in more fungible assets than a home. Owning a home ties you to a specific location, and can't easily be sold in an emergency. Plus it's not a very diverse portfolio if most of you wealth is in a single property