> If I buy BTC with USD and then transfer it to an exchange with a BTC/USDT pair, I'm not suddenly "short USDT".
It does, it just doesn’t make you short against USD which is what you’re thinking of. It only makes you short vs. BTC which we expect to collapse in price as well. This is why you need the other leg.
> So I don't see why buying BTC with USDT directly makes me short USDT either if I didn't borrow the USDT but bought it with USD
Which is why I keep talking about margin and perpetual swaps. Since we expect to lose our shirt on Binance, we need a levered position which means borrowing the USDT which will ultimately become worthless. This borrowing happens implicitly in a swap or future.
Back to your first question, when you buy something, you’re going to denominate that in some unit of account. We usually write this price as saying asset A is $X or asset B is €Y. But in reality every market is two asset pairs, no different to FX or crypto. We could have talked in terms of A/USD being X or B/EUR being Y. It’s just a different convention.
So when we talk about (for instance) the price of AAPL stock, what we really mean is AAPL/USD. Or when we talk about the price of crude oil we really mean CL/USD. I am buying AAPL, selling USD. Or I am selling crude oil, buying dollars.
To illustrate let’s say that you’re long AAPL (AAPL/USD). If shortly after you buy AAPL, the dollar loses purchasing power versus all other currencies, net net we would expect AAPL to go up in price (otherwise known as inflation). It’s not that AAPL became more valuable, it’s that the USD became less valuable. So you’re implicitly short the dollar. You sell your AAPL, and pocket your profit. You could frame this as being short USD and then covering your short. Same thing.
The opposite also holds true. Let’s say you short AAPL (remember: AAPL/USD). This leaves you long USD. If the purchasing power of USD increases, ceteris paribus, the price of AAPL should fall (otherwise known as deflation). You cover your short, and pocket your profit. You can view that as being short AAPL and AAPL going down, or you can view that as being long USD and the dollar going up. It’s the same thing.