My impression is that it has to do with the role of one's ego in life, considering the sentences that follow. I think that a large part of getting older and wiser is to better understand your place in the universe as merely one small part of an impersonal universe, as opposed to feeling like you're the center of the universe.
I think we hold way to dearly on to the idea that it is only our experience that matters. So I interpret "impersonal" as less about oneself or one person.
"We insist on ourself as individual agents in the world - it is the story we trap ourselves in."