When it comes to sending Bitcoin, Coinbase does charge a fee. This is because when you send Bitcoin, the network will actually charge a small fee for the transaction. Coinbase will then pass this fee onto the customer. The amount of the fee will vary depending on how much Bitcoin is being sent and the current market conditions.
However, it is important to note that Coinbase does not make any money off of these fees. They simply pass them along to the customer in order to ensure that the transaction goes through smoothly.