For most Americans, who move around fairly often, they will never come close to paying off a mortgage and the only equity they will ever own will be what they bought with their down payment plus whatever they get on the margin if the value of the house goes up.
If you, say, live in a house for five years and then move, then you basically rented the house from the bank for five years. Except that unlike a renter you also assumed the (upside and downside) risk of home value change, and assumed the cost of taxes, maintenance, etc. Plus you tied up a large sum of money in a down payment.
This may be worth it if you want to bet that home prices will go up in the next five years. It also may be worth it because mortgage interest, unlike regular rent, is deductible from your taxes, which is perhaps the most obscenely regressive thing in the tax code.