You also are missing the point.
At any given instant, your monthly payment for a 15-year will be higher than for a 30-year. You're right that if you can't afford it, then you shouldn't do it.
If you can possibly afford the payment for a 15-year: in 15 years you'll have a monthly payment of zero, because you'll have paid it off. After a few years, you'll have started paying off the principal.
And, of course, if rates go up (as they have), then in a few years the monthly payment for the 30-year will be approaching what you would have paid a couple years ago for a 15.