It all boils down to fractional reserves in an illiquid market. If you're keeping the USD in a bank and issuing a coin representing it, no problems arise, because you'd effectively be acting like a bank.

In Tether/iFinex's case, you have a situation where there was a "pseudo-bank" (Tether) and a crypto exchange (iFinex) that were highly intertwined. Because Tether was more or less controlled by iFinex, which also controlled one of the largest cryptocurrency exchanges by volume, this provided a unique cover for fraud, and different profit motives than a traditional bank would have. Tether did its business by exchanging USD for Tethers. iFinex did its business by pocketing spreads and fees from crypto to crypto trades. Meaning, Tether had a bunch of USD on hand, and iFinex had a bunch of crypto (primarily Bitcoin) on hand. What likely happened in Tether's case was that iFinex instructed Tether to create unbacked Tethers out of thin air, and used these Tethers to pump up the value of iFinex's own Bitcoin holdings. For example, suppose issuing $1M of Tether and spending it on Bitcoin moved the spot price up enough to increase the value of iFinex's Bitcoin holdings by more than $1M. Isn't that basically free money? You've spent $1M and created more than $1M in paper value. All you have to do is sell those Bitcoins at the new, higher price for real USD, and you've made relatively risk-free profit.

Why the hell did this work for so long? First, the market believed Tethers were backed 1:1 with USD and treated the two as functionally equivalent. Some traders would see the Bitcoin price increase on a Tether exchange like Bitfinex, and then buy Bitcoin at nominally "cheaper" prices on non-Tether exchanges like Coinbase, so that they could transfer the coins over to Bitfinex and sell them for a tidy profit. In this way, the Tether exchanges could impact Bitcoin's price even on exchanges that didn't use Tether due to the natural incentive for arbitrage. Second, the crypto markets are quite illiquid, and because orderbooks are thin it only takes a small amount of buying or selling firepower to push prices pretty drastically. The alleged fraud is that iFinex did exactly that, and progressively pushed prices up. Third, as prices swelled, Bitcoin attracted more _real_ investors, and many such investors then spent actual USD on Bitcoin, creating a self-fulfilling prophecy that in theory would have enabled iFinex to totally get away with it - all they had to do was sell off enough Bitcoin to cover for all of those unbacked Tethers they'd issued, and they would essentially become whole.

Now, things get interesting when it comes to how iFinex ran its business. iFinex refused to implement KYC/AML checks on their exchange, because nominally they were "crypto-to-crypto" and thus considered themselves to be outside of the US financial system's jurisdiction. In practice they used an indirect relationship via one of Wells Fargo's affiliates for a long period of time until they were found out, and then the US financial system more or less put a moratorium on doing business with them. It turns out that being locked out of the US financial system is extremely damaging when your customers want to withdraw US dollars, so for a period of time, iFinex tried jumping around from bank to bank, trying to stay ahead of regulators who had effectively blacklisted them by having customers making deposits wire their money to pay off other customers looking to withdraw money, and all kinds of other shady practices. Eventually they ran out of options and started doing business with what looks to have been a money laundering shadow bank, Crypto Capital Corp, who then promptly stole a bunch of their money, which then led to the current debacle.

All told, it's one of the most interesting stories in the financial markets by a long shot. It will be fascinating to watch it continue to play out.