Why can't a Business Partner level user see the "Business Partner" drill down option under the User List section on the User Profiles screen?
Enable the following option on the on the business partner level user's profile, for them to see the "Business Partner" drill down option under the User List section on the User Profiles screen.
Navigate > Configuration > Security > Security > User Profiles
Important! Only a business partner level user with access to the "Business Partner" drill down option can make this change.