Metamask is connected to Avalanche's C-Chain. Exchanges are connected to Avalanche's X-Chain. Because of that, you cannot directly send your funds from Metamask to an Exchange. Any attempt to do so directly will probably end in a loss of funds.
To deposit your AVAX from Metamask to an Exchange, you first need to get your funds onto the X-Chain. You can do that in the Avalanche web wallet. You can create a new account in the web wallet and send your funds to the C-Chain address of the newly created wallet, shown next to the balance panel when you select 'C' tab. Alternatively, you can open the account used in Metamask in the Avalanche web wallet, by logging into the wallet with Metamask private key (or a Ledger device if you use one in Metamask). To get the private key, in Metamask press three dots next to the account title and in the menu select account details:
On the details screen press 'Export private key'. Use that key to log into the Avalanche web wallet by selecting private key as a login option. Be very careful with that key and store it in a private and secure place, as that key is used to access your funds!
Now that you have access to the Avalanche wallet where the funds are (either by accessing the Metamask account, or sending from Metamask to wallet's C-Chain address). Select the Cross Chain tab in the wallet, and select C Chain as source, and X Chain as destination:
Transfer the funds from the C Chain to the X Chain. Now you are ready to transfer the funds to an Exchange. Follow the instructions from their website to send the funds form your X Chain balance to their deposit address.
PLEASE NOTE: You cannot use this procedure to send any other tokens besides AVAX. Attempts to do so might end up with a loss of funds!