Earlier quoted context omitted.
The idea is about trying to keep seperate the things you do/feel/believe and what you are . For our waiter friend, is the fact that he's a waiter somehow the essence of his being? Or is it a job he does, because one needs a job and this is on balance a pretty good one? In the latter case, if someone says that waiting is a dead end job, he can much easier say sure, yeah, not many places to go, but the hours are really…
I agree that it would be more productive for the waiter to be able to detach his identity from his job. But to even be able to do that in the first place, he needs to have something else going on. He needs to be so sure of his identity that an insult to his line of work doesn't bother him. But if he's taken the writer's advice, and kept his identity very small, what if he one day realises that whatever he saw himself…
I think this is indirectly a large part of the problem. The trend in society is that everybody must have totally unique and interesting identities, and since few people are in fact "special" enough to live up to that ridiculously high standard, they need to pile on everything and the kitchensink to get to some reasonable approximation. And you'll still wake up one day and dread that your identity is not, in fact, unique and interesting enough, which looks a lot like your "a lie" scenario. But in the meantime, you've set yourself up to spend a non-trivial amount of time fending off attacks, real and imagined, on any of the myriad of items that make up your identity.
In a past not too distant, our waiter-friend would be content to see himself as a good person, a good friend and a provider for his family.