Please go on. Could I have an example?
Ay. There's the rub. I won't PL, I'll only say that some areas are extra-unpleasant.
Sure. The key difference is that you get something extra for your money with a mortgage, and that something extra is equity.
Your rent is $2,500 a month all inclusive, meaning you pay $30,000 a year in rent.
Let's say you could apply that $2,500 to a mortgage payment instead. Take $350 off to account for taxes and utilities and/or condo fees, so $2,150.
What does that mortgage look like? Well, let's take a relatively bad interest rate of 4% and 10% down, amortized over a 25 year period--I'll spare you the math, but if you have $45,000 saved, you can get a mortgage on a $450,000 house for that kind of payment.
So, same payments, two different places, except on one you're paying rent and on the other you're paying a mortgage. Not much difference at first--most of your mortgage payment is going to be interest at first, but as you start to pay your mortgage, you start to repay the principal on that mortgage loan. Since you've reduced the principal of the loan with that first payment, the interest is less on the second payment, and so more of your payment goes toward paying down the principal. More and more of your payment goes toward paying down the principal as you make more and more payments, until 25 years later you've paid it all off.
What do we have at the end after paying the same payments for 25 years? Well, the renter has nothing, and the buyer has a house that they can sell, or refinance, or whatever. Chances are also really really good that that house is worth a lot more than he bought it for too. For simplicity's sake, let's say the house hasn't gained any value in the 25 years you've owned it.
When would you be better off not buying a house? Well, since you can cash out your equity in the house at any time, the only way it would make more sense to rent your whole life is if the total interest payments exceed the rent:
25 years of rent @ 2,500/mo = 750,000 payment
vs.
25 years @ $2,500/mo + down payment @ $45,000 - value of house @ 450,000 = $345,000 payment
So, even under these very pessimistic circumstances, it makes much more sense to buy than to rent. Interest rates and house prices would have to be very high and rent would have to be very low for it to make sense to not buy.
For people with extra money, this is why real estate is an attractive investment. Often, the rent payments can cover most of their mortgage payments and they get a free house at the end. See discussions on the "capitalization rate" in your city, a real estate specific term for the yield, for more in depth discussion. Very roughly, the difference between cap rates and interest rates, plus the value of the property, is the profit an investor can make on renting a property over the term of a mortgage.