The ability to Associate Interests is tied to the Contact Management permissions.  Identify the user's administrator group and update the permissions for that group:
  1. Navigate to Constituent 360 > Groups > "Administrator Group List" tab > Click "Edit Permissions" next to the group in question.
  2. For the permission type, choose "Contact Management".
  3. Choose the option to View Non-Sensitive Contact Data.
Make sure to have affected administrators logout and then log back in again to experience this change.