Logic behind uncovered interest rate parity?

So I am having trouble understanding the UIP equilibrium condition. Namely, according to UIP, when the home country has a higher interest rate than the foreign country, its currency will depreciate over time. This is highly counter-intuitive to me, since I would expect higher interest rates to increase demand for the home currency, thereby raising the currency's price, leading to an appreciation of the home currency. What is the mechanism that would lead to the home country's currency depreciating? What is the logic behind this?

There were similar questions on this forum, but I did not find an answer that could explain it well to me.

An example with USD($) and EUR(€): Suppose $$1 + i_{} < E_{€/} \cdot (1 + i_{€}) \cdot E_{/€}^e$$ Then traders are incentivized to take dollar loans, convert this to euros, collect the euro interest, and convert it back to dollars. Due to the trades there will be more present day demand for euros, making euros more expensive in dollar terms. Thus the €/\$ exchange rate will decrease. (You get fewer euros for a dollar.) In the future, when the traders reconvert euros to dollars repay their dollar loans, the trades create more demand for dollars, making them more expensive in euro terms, thus the expected \\$/€ exchange rate will also decrease.