A primary filter cannot be deleted from perspective.
The difference between "Primary" filters and secondary filters is that the former are categorizations (rules built using the Categorize option which are fundamental to the dynamic rule) and the latter are individual searches (the Search option). Because of the way perspectives, specifically dynamic perspectives are built, categorizations can't be changed because they apply to the entire perspective block at once. To edit one would be to change the whole dynamic block. The secondary filters apply only to that one specific perspective group and can be edited however you need, since they only apply to that group.