Actually, there is no concrete scientific evidence that braless breasts sag (Some sources even claim that the opposite is true and that they may even cause cancer o_o!). We have to remember that breasts don't contain any muscle tissue, so in essence, it would be impossible to train them with a bra :p.Man boobies sag.
Khrushchev:
And… Ah-nold :(
Arnold had muscle under his once though. But mainly I think it's skin stretching. I do know that you can stretch skin to pretty much any amount, given time and pressure/weight, and it's impossible to shrink it back afterwards (without some judicious tailoring). So maybe that's the reason for sagging chest flesh?
Not that a bra would do too much to arrest that, unless you wore it pretty much permanently.
The main reason for a bra is to create the impression of a particular bod-shape under clothes. In that way they're exactly like old corsets and hoopskirts, except a much lighter less restrictive version.