It means that he is chasing an illusion, or he is chasing an illusion, something from his imagination which is not real.

I like that song! "Now you're out in the world Searching for your soul Scared not to be hip Scared to get old Chasing make-believe status Last time you felt free Was when non of that sh** mattered 'Cause you were with me" In my opinion, she is talking about a person who used to feel emotionally secure and "self-accepting" when she knew them. And, now that they are separated, this person's soul feels lost and they are striving to find their place in this world solely through the acceptance of others <3

He's chasing social status (that's the "status") but make-believe means not real, fictional, imagined. So basically he thinks he's chasing something real and she's saying that getting social status won't really mean anything valuable or worthwhile, and that even if he get's social status it won't make him happy (because he doesn't have her ;) )

'' believe status " means how rich or poor you are.

Sorry for the error ("non", I meant to type "none"). Basically, "make-believe status" in this context is a "social status" that doesn't align with this person's true self.