Thinking of a recruiter as a teacher doesn't seem accurate to me. They should not be expected to understand the company well or the role of the software team in the company.
Recruiters are intermediaries whose role it is to save the hiring manager's valuable time. They will focus on the initial scanning of profiles (does this vaguely look like a developer profile?), be responsible for scheduling and maybe salary negotiations as this means you can start a fresh relationship with your hiring manager without the potential tension left over from a salary negotiation.
The exception are executive search professionals who will understand the business model well, but even they would not be able to recommend a book.