So just to make sure I understand, when BitFinex offers leverage trading, are they betting that the price of Bitcoin won't go up as high as the folks asking for leverage think it'll go?
If not, why do people offer leveraged trading? Just for the interest? A fee?
A broker offering leverage is earning interest nearly risk free. They retain control of the collateral and can (as observed) force close the position. Only in really extreme situations is their money at risk.
Correct, but it is actually other users offering the leverage. Bitfinex created a P2P market for it. If you offer your USD as leverage then you receive interest.
If not, why do people offer leveraged trading? Just for the interest? A fee?