In database systems, to drop an index, you must either be the owner of that index or have the DROP ANY INDEX privilege. This is a security mechanism to prevent unauthorized removal of database objects.
In Oracle, dropping an index you don't own requires the DROP ANY INDEX system privilege, which grants the ability to remove any index in the database regardless of ownership. There is no DROP ALL INDEX, REMOVE ANY INDEX, or REMOVE ALL INDEX privilege in Oracle's privilege model — those are distractors using plausible-sounding but nonexistent names.