When you trade forex you never actually take possession of any currency. Spot forex is based on a 2-day forward exchange agreement. In other words, today you agree to do the exchange in two days. You never actually get to that exchange point, though, because (assuming you carry the position overnight) your broker keeps rolling your position forward by offsetting today's transaction (doing an opposing transaction) and opening a new one. This is call rollover and it happens at the end of each trading day. Some brokers do it very overtly, others almost transparently.

So when you go long EUR/USD you never actually exchange USD for EUR. Nothing comes out of your account and nothing goes into it aside from the gains/losses on your trades.

That all said, your profits/losses are based on the idea that you are borrowing the short currency (USD), converting it to the long one (EUR) and depositing that currency - which is where the carry comes from.

In terms of your friends example, it's find for the stock market, but not for forex because while in stocks an exchange of possession of the stock actually takes place, that doesn't happen in forex. Think of being long as benefiting from appreciation and short as benefiting from depreciation and you will be much better off.

And remember that in forex you are always long one thing and short the other. As in the EUR/USD example, you are long the EUR and short the USD. That means you gain by appreciation of the EUR and you gain by depreciation of the USD (relatively to each other, obviously).