The buy/rent decision is quite complex for many reasons, but two overlooked factors are:

1) When a bank loans you $1e6 to buy a house, they are effectively deputizing you to act as a money manager: they allow you to make an investment that will hopefully appreciate more quickly than the interest rate. There are many other investments that have this property (e.g. the stock market), but banks won't loan to you to invest in them!

2) A mortgage acts as a forced savings rate: you pay the bank every month, and when you're done after 30 years, you have a large asset. So a large mortgage is (for some people) a good psychological commitment mechanism that imposes financial discipline.