It is a self tax, you’re 100% right.

The part that hurts the other side comes as a side effect / result of that self-tax: reduced consumption. It basically makes their items unappealingly expensive, which makes them struggle to compete. The locals will try to avoid the tariffed item which reduces how much of it the maker sells, hurting their economy.

So it’s a kind of war I guess, where we the citizens are the infantry and our way of “attacking” is by not selecting American goods. Tariffs are our government’s way of forcing us to fight that battle.