I feel you don't know how an exchange work.
You need to know the difference between an exchange and a non-custodial wallet.
If you hold your bitcoin on a non-custodial wallet, you have full control over your fund. If you want to make a transaction, your wallet needs your private key to sign the transaction.
If you want to withdraw a fund from the exchange, you don't need any private key. Because you are not the one who makes the transaction. You request the exchange to make a transaction and the transaction is signed by the exchange not you. In this case, the private key is owned by the exchange.
Your bitcoin address is what you need to receive bitcoin.
Let's say you want to send me bitcoin. I give you my bitcoin address and you send me bitcoin.
Whoa! Hold on. Is there a difference (when talking about keys and addresses), between Bitcoin and other coins?
What I've seen is that, to transfer your coins from your exchange wallet to your software wallet, you use your software wallet's public key, and to transfer funds from your software wallet to your exchange's wallet, you use the exchange wallet's public key. Basically meaning you can keep your funds safe by
never using your software wallet's private key. Do you need both?
NeuroticFish: thank you, I will read it. I know Exodus is not 100% open source, but Electrum is for Bitcoin only, and I intend to invest on several different coins. That's why I was interested in EToro, buy it's now out, as it offers a download button that downloads nothing, and instead tricks you into opening an account with them.