When trying to delete an Affiliation from the Sphere of Influence section, the following error occurs even though the user has Delete permission on the Affiliations_vod object: You do not have permission to edit or delete this affiliation.
This error occurs because the user does not have Field Level Security (FLS) for the Destroy_vod__c field on the Affiliation_vod__c object.
The Destroy_vod__c field is a system field used by the update trigger to delete the affiliation (and its child or parent) regardless of the owner of the affiliation. Without this trigger, users can only delete affiliations that are created or affiliations that are owned by those lower in the role hierarchy. When the Sphere of Influence wants to delete an affiliation, it uses this Destroy field rather than a delete API call.
Note: Do not expose this field in the UI.
Grant user Read FLS for the Destroy_vod__c field on the Affiliation_vod__c object.
CRM Help Documentation: Sphere of Influence