Can't compare mortgages and rent.
When people speak on having an inexpensive mortgage, that's usually the result of putting a decent sized cash payment down on the house. You have to remove some chunk of your own liquidity to "buy in" so to speak.
Apples to apples would be if you compare your total costs (mortgage, property taxes, repairs, insurance, HOA fees etc) to paying rent....not just mortgage vs rent.
In Dallas...property tax on a modest $250k house is like 5,000/year. You can rent a decent apartment for $1,000-ish. So five months rent plus a mortgage and everything else.
Having said that.....owning IS BETTER long term if you have enough money. If you are iffy on cash, better to rent and be flexible/liquid. Owning is good when you have enough dough where you could put maybe 1/3 of your savings into a down payment and have it be a significant downpayment. If you have to wipe out your savings, brokerage and 401k accounts....bad idea.