These buy vs rent calculators assume that any savings made from paying rent instead of mortgage is paid directly into an investment account. I.e. you sock away the full theoretical mortgage amount less rent paid into a managed fund or some such.

The reality that I've seen is that people never actually do that, or at least not to the full degree, and treat the difference as extra disposable interest. And so the money gets frittered away and the calculations are wrong.

You can't do that with a mortgage: you have to pay it, and so therefore people have an enforced savings/investment discipline. And also the incentive to sock as much money into their house as quickly as possible, to pay down the debt.

So the money side is generally better, and you generally get a better house, when buying. But it's a bit of a commitment which some people will avoid on principle.