Why is the argument often brought up that people will not want to pay for coffee with BTC, because they expect its price to appreciate?

I don't get it. Let's say a cup of coffee is $3. That's 15675 sats today. What difference to your future wealth potential does it make if you pay with sats or dollars?

If you pay with sats, you have less BTC and will miss out on the gains from its future appreciation.

But if you pay with dollars, you have $3 less to invest in BTC and benefit from its future appreciation. If spending BTC on coffee is stupid, so is spending dollars on coffee, because every dollar spent on coffee is a dollar not invested in BTC.

A more interesting argument to make would be: in a world where Bitcoin exists, why would anyone buy a cup of coffee and NOT invest the same amount in BTC?

The short answer: the existence of a store of value like Bitcoin can lower people's time preference and make them consume less. Still, they will continue to buy coffee, because, well, they like coffee.

That, however, has nothing to do with the form of payment used. If you've already decided to cough up $3 on a cup coffee, you can as well pay with BTC, which as a payment rail has many advantages.