Hmm currency.
Is bitcoin a store of valuy? I guess not? The only intrinsic value it has is the ability to move value around.
You can store value in it. Even fiat currency fluctuates. If you store your fiat money in a bank it likely wont have the same purchasing power by the time you retire.
If you do not exchange value into bitcoin i.e. USD/BTC it would be worthless.
Wrong. You can buy plenty of things with it or just hold it as an investment. Is fiat money worthless if you don't spend it?
it is a medium of exchange, which does not make a currency. Blockchain is a payment rail and bitcoin is medium of exchange.
It's all of those things.
Or explain to me what makes it a currency?
The fact that you can buy things with it and people accept it as payment for things, therefore a currency.