You're taking on debt. There is a risk associated with that debt.
True, but it doesn't follow that one is living beyond one's means by taking out a loan, whether it be for a car or a house ("mortgage.")
The problem has already been described well: People buying too much house and then piling on student debts, credit card debts, multiple car loans and failing to reconcile their income against the debt load they take on.
I'm among those that are debt free. No credit card debt, no auto loans, no mortgage. My wife and I bought modest in an affordable city and while we had two cars, both were older, cheap beaters we used while we put every cent toward the house. We didn't actually have a mortgage; we had a substantial down-payment from previous savings and used a line of credit for the house. We didn't eat at restaurants, didn't furnish the place with the fanciest stuff, didn't put in the $50,000 kitchen etc. I had an electronics business as a 2nd job at the time and put most of my income from that into the house. We paid it off in just a few years. My wife celebrated with a new car in 2005 & paid cash; she still drives it now. My Subaru was fairly expensive but used; paid cash. My Fazer was used; paid cash. My CBR was new but pretty cheap; paid cash.
Going by property assessments our house has roughly doubled in value compared to what we paid 16 years ago (at least in absolute dollar terms...) The debt we took on was certainly not a bad thing or a sign we were living beyond our means. We carefully approached and managed the debt and came out smelling like roses.
If something bad happens, there is a possibility that you could lose the house.
If "something bad" happens and you can't pay the rent on your apartment you're just as out-on-the-street.
I know a few people that have bought houses cash.
Must be an incredibly rare thing. Maybe such people come into an inheritance or had shares in a start-up that was bought by Google. Or maybe they took a risk, got a mortgage on a fixer-upper, flipped it and made a bundle and rolled that into another house etc. Hard to picture someone saving a quarter million dollars or more in a reasonable amount of time by socking a bit of each paycheque away each month.