You’re most likely using GMail for sending your message. See GMail’s documentation.
If you’re sending mail to a mailing list that you subscribe to, those messages will only appear in ‘Sent Mail.’ This behavior also occurs when sending to an email address that automatically forwards mail back to your Gmail address. To test forwarding addresses or mailing lists, use a different email address to send your message.
When a message from firstname.lastname@example.org, for example, goes through a route:
email@example.com -> firstname.lastname@example.org
When this message arrives to GMail, it will have email@example.com as both sender and recipient, therefore GMail will not show it.
In other words GMail does not show you messages you sent to yourself.
The other possibility is that the address had previously experienced a Hard Bounce and is on the ‘do not send’ list. Check the Bounces tab for a list of these addresses and remove the address in question if it is there.