A knowledge base article about Why can't I create or add direct members to a SPA? provided by the UC Berkeley IT Service Hub - Knowledge Portal
Any UC Berkeley employee should be able to create a SPA; if not and you are a member of multiple SPAs, double check that you are not logged in as a different one.
To create or manage a SPA, you need to be logged in as yourself.
Please note that Graduate students are unable to create SPAs, though they can be added as direct members and delegated access.