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, a message will appear after clicking Remove User that states why the User cannot be deleted. For example:"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."

Another reason this may occur is if the user is listed in another user's emergency contacts. In that instance, you can fix this by manually removing the user, under Core > Users > Edit User Profile Data > Remove User, where you will see the message "The current user is listed as an Emergency Contact for the following user(s) and cannot be deleted. Clicking 'Drop Current User From This User's Contact List' will allow them to be removed since they are not able to be merged:

One reason is that two records cannot be merged if both users have a started application. This would be true for any records with applications attached to them. Additionally, a Candidate Role cannot be merged into a Student Role.