Vantage user cannot delete Skill in their tenant. Corresponding icon is absent in the interface.
User account has insufficient permissions for Skill deletion in the tenant.
In Vantage 2.1... versions, users with Skill User and Skill Designer roles are not allowed to delete Skills. Only Tenant Administrator is allowed to delete Skills in the Skill Catalog.
In Vantage 2.2 versions Skill Designer role and Tenant Administrator role both allow to delete Skills.
Use user account with proper permissions to delete Skills.