There is a solution to the housing problem besides home ownership and renting: Housing cooperatives. These are still relatively common in Germany, my parents live in a flat owned by a cooperative and are consistently paying less rent than I pay for my college dorms, despite living in the center of a major city.
The cooperative was founded by workers in the 19th century and has a single purpose: To provide affordable housing, satisfying the needs of their members. It isn't subsidized by the state, its business model is simply to distribute the expenses for building and maintaining the flats to their members.
Home ownership has the disadvantage of being too inelastic and imposing the risks of owning a house to individuals. Renting from a private company on the other hand means you constantly have to give up a significant portion of your income so someone else makes profit from basically doing nothing.
Cooperatives strike me as the best solution to this dilemma. It's of course not surprising that the Economist doesn't mention this at all, the flaws of their argument have been sufficiently demonstrated by other commenters. The basic recognition that home ownership is flawed is an important point though IMO.