You cannot delete the association types that CentraSite provides out-of-the-box (not even if you belong to a role with the Manage Asset Types permission).

You can delete an association type only if there is no relationship attribute defined with it in the catalog. After a association type has been assigned to a relationship attribute, it can no longer be deleted.

You cannot delete the stand-alone association type that is in use for defining an association in the catalog.