Counting senders in a mailbox
In some sense, you haven't really completed the task, which is to find the most prolific commenter.  Your get_email() function requires you to know the names before you call the function, and to know what those names are, you would have to read the mailbox!

Furthermore, your user dictionary is kind of pointless.  It's only ever used as a write-only variable user['email'].  And since only one key is used, there is no advantage to using a dictionary rather than just a regular variable.

To do the job properly, you should make one pass through the file, keeping track of the counts of all of the users as you go.  Using a dictionary to accomplish that is the point of the exercise.