but what is the "promise". Can I sell it back to Tether for a dollar? I assume not. So I don't understand what the point of this "promise" is if it's traded on an exchange like every other coin
Exactly. Which is why many have cautioned people to stay away from centrally issued stablecoins such as Tether.
There are also attempts at decentralized stablecoins, but it's not an easy problem to solve:
https://bitcointalk.org/index.php?topic=3421190.0[...]
The more interesting thing is to see what the collapse of Tether does to the price of BTC. If there is a somewhat orderly exit from Tether (this is what is happening right now) and the position is unwound then when it does collapse the impact may not be significant. But if Tether lets go in a hurry, and it probably will, then expect to see some carnage. BTC is yet to prove it's worth as anything more than a gambling platform and if people don't think they can win at any odds then they probably won't want to play the game.
That depends which way the money leaves. People selling USDT does not equate people leaving crypto for good. Currently the majority seems to flow towards BTC, rather than USD:
https://coinmarketcap.com/currencies/tether/#markets