Here's what you're missing:

The USD:USDT exchange rate should always be 1:1. If 1 USDT is, due to market pressure, suddenly worth $0.98 USD, Tether's responsibility involves some analysis of either waiting for the market to resolve itself (maybe its a transient thing, and its an arbitrage opportunity, so The People may step in), or act as the source of market liquidity; they buy USDT up, with their dollar reserves. Now they, as they always do, have a reserve of USDT they can re-sell for $1 USD without minting new currency, which is convenient (though ultimately a liability on their balance sheets).

But there's a second situation: the exchange rate hits 1 USDT == 1.02 USD. This would happen if demand for Tether were very high; people want safety and stability, so they demand USDT. But: they aren't interested in "leaving crypto"; they don't want to convert USD to USDT, they want to convert crypto assets to USDT. The open market doesn't have enough liquidity to support the 1:1 exchange rate, so the price of USDT starts rising.

This absolutely happens in exchanges which price crypto assets in USDT, which is many. One exchange says 1 BTC = X USD, another says 1 BTC = X*1.01 USDT, and there's now an inter-exchange arbitrage opportunity based on the promise that 1 USD should be 1 USDT. That arbitrage, in some market conditions, can act as an upward force on the price of USDT.

It is ALSO Tether's responsibility to cool off the market. What do they do in this situation? There's only one solution: they need to increase the liquidity pool of USDT. In other words, there are sources of demand for USDT outside the scope of the purist viewpoint of "give me one USD and you get one USDT" rooted in their responsibility not just to act as a reserve bank for USD/T, but also a market maker. Markets misbehave; Tether promises stability.

What's the source of these USDT? They probably have some USDT in their reserves. But beyond that, they need to be minted! Their promise is that every minted token is backed with USD. Assume they're keeping their promise, then follow the line of questioning into where the USD comes from. Return on USD investments for sure. Bank loans? External investor capital? CEO working nights at McDonalds? Regardless, it gets minted and then sold (probably at $1 USD); they make the money back.

And, of course, there's the situation if that assumption is wrong. They have no external source of capital; they just mint tokens to meet demand, hoping that they get sold at $1 USD to refill the reserves. And that's damn convenient, wouldn't it be? USD-backed investments are pretty risky; we could be in a down market and their AAPL shares are in the red; and its USUALLY the case that demand for USDT, for stability, would be high when other markets are in the red; when it rains it pours. They need to pay taxes on the ROI of those investments. Things like bank loans or external investor funding usually also have expectations of ROI. Those are all costs; and it would be REALLY convenient if they could just ignore those and mint the tokens, who cares, the money will flow back in.

This actually works most of the time; it's literally called Fractional Reserve Banking, and everyone does it. But during black swan events, it can break down; especially when you mix in typical finance bro greed, but that isn't even necessary for something like USDT to break down.

There's no perfectly safe way to create a reserve-backed stable asset. The best hope in a deflationary context is that if the price of USD:USDT goes to something like 1:1.01, people preemptively come to Tether, give them USD for USDT, then arbitrage it back to 1:1. But because the logistics of doing that are different than just exchanging crypto-to-crypto (latency, KYC, etc), there could be a demand mis-match. Tether can't let the price stay above 1:1 for long, because it actually devalues the USD basis of anyones' investments denominated in USDT, which is a loss-of-faith event that can spiral to be even worse. So Tether steps in.