There are two reasons I'm guessing the author doesn't see himself as part of the working class.
1. He doesn't make fun of the working class like he does to the other two. Either because he doesn't know them well enough to do so, or because he doesn't want to insult them.
2. The UAW locals in the Bay Area represent graduate students, postdocs, and nonprofit workers. No one in "service jobs or government jobs" or "nurses, teachers or craftsmen."