Just a note about this: We had previously requested that messages show up in your inbox if you include yourself as a recipient: Have PMs show in inbox if you include yourself as recipient.
If messages you send to a group also show up in your inbox in the case you are a member of the group, I also think that makes sense (and would be consistent with other similar tools, like email, I believe).
If all messages you send–even ones to individuals where you don’t include yourself, or messages to groups that you are not a part of–also show up in your inbox, then I agree that would not be the appropriate functionality.