Merge Accounts will delete the "New User" and update the "Existing User" based on the differences noted. 
This error may occur if one of the users being merged has Course Requests or an Application. Additionally, a Candidate can only be merged with other Candidates, not Students

To determine why you are unable to merge duplicate users:
  1. Core > People Finder > user > Access tab
  2. Click Remove User
  3. Once Remove User is clicked, if the Delete option appears, do NOT click Delete.
  4. If a user cannot be removed for any reason, an error message will appear after clicking Remove User that states why the User cannot be deleted.
The error messages below may be returned to explain why a user cannot be deleted:

Error: To permanently remove this student, all school registration rows must be deleted first. An alternative is to withdraw him/her and assign the Past Student role.
The user has student enrollment rows that must be deleted.
1. Go to Core > People Finder > [user] > Access tab. 
2. Select the Edit icon next to the Student persona and select Edit school enrollment
3. Delete all of the enrollment rows. If an enrollment row cannot be deleted, see Delete button is missing or grayed out when attempting to delete student enrollment row.
4. Once all rows have been removed, try merging the users again.
 
Error: The current user is listed as an Emergency Contact for the following user(s) and cannot be deleted.
The user is an Emergency Contact for the user listed in the message. 
Select Drop current user from this user's contact list to remove the Emergency Contact entry.

    
Other reasons that two profiles cannot be merged include if both users have a started application. Additionally, a Candidate Role cannot be merged into a Student Role.