It's because you have Quick Reply mode enabled for your Facebook Messages. When Quick Reply mode is enabled, it will send a message when you hit the Enter key.
If you don't see a "Reply" send button when typing your facebook message, then Quick Reply is enabled. Just below the reply message box, there is a Quick Reply checkbox, that when checked will Turn On quick reply.
So to Turn off or disable Quick Reply, simply uncheck the Quick Reply checkbox. Now when you hit enter, it will put the cursor on a new line (or paragraph), instead of sending a message. You should then see a "Reply" button, which you will need to click to send your message.