The other is deleting a message that was sent to someone else from _their_ inbox. Which email does not allow you to do.

Except some clever people tried to implement this (notably Outlook and/or Microsoft Exchange has such a feature IIRC) where it sends another email to "recall" the earlier message. It's funny when you receive those recall messages in a non-Microsoft email client and on a different server than the Exchange sever they're using. I.e. you just ignore their request to recall and now you _really_ go read the message they're trying to recall, because it makes it _more_ interesting. Also googling this quickly it seems even if you stay completely within the Microsoft ecosystem it only works if the recipients didn't open the original email yet:

    With message recall, a message that you sent is retrieved from the mailboxes of the recipients who haven’t yet opened it.