As I understand him, Michael Hauge mixes up the "mentor" from the Hero's Journey approach to storytelling and the function that secondary characters have for film.
From your other questions I believe that you are writing novels, not film scripts, Tom. To answer your question you need to consider one of the fundamental differences between novels and films (as they are made in Hollywood). In Hollywood movies, there is usually no self-reflection, because the movie is filmed from the third person perspective and we don't have a voice-over with the protagonist's thoughts. The effect of this is that characters in Hollywood movies are usually black boxes (in the behaviorist meaning of the word) about whom we know nothing but their observable behavior. For these characters to have depth, their thoughts and other cognitive and emotional processes have to be externalized in the form of interpersonal behavior: they tell another character how they feel, they discuss their ideas, and so on. That is one of the most central functions that the characters that surround the protagonist have in a movie: they reflect his or her mind both to the viewer and to the protagonist him- or herself, so that the viewer can witness how the protagonist achieves understanding and development.
In a novel on the other hand you can convey anything you want in the narrator's words. The narrator can directly tell the reader what the protagonist thinks. So the author can show the protagonist "doing self-reflection" and growing by the power of his or her own understanding. He doesn't need someone to do mental ping pong for the reader to see how and why the protagonist grows.
In a novel, you don't need the reflective function of the secondary characters, at least not necessarily, but if you write in a "cinematic" style – avoiding internal monologue and focussing on what a camera might see (often called "show, don't tell") – you can of course employ this filmic device in writing, too.
The function of the mentor is to teach the hero something about him- or herself. That is "reflective", in a way, but his function goes further than just being a more or less random conversational partner. The randomness is made visible when in some movies the protagonist talks to the mirror or an animal as reflectors. The mentor on the other hand does not just provide an opportunity to self-reflect, but has understanding and conveys it, though usually in an indirect manner, similar to a psychotherapist who puts obstacles in the patient's path until the patient finally understands what he does wrong and how he can change. The mentor and the friend are extremes on a continuum, with the friend providing an opportunity to "talk things through" and self-reflect, and the mentor providing a learning experience.
In my understanding, the mentor (or other "reflective characters") do not fight against the hero, but they might (verbally) fight with the hero in their struggle to get the hero to understand.
In some stories the hero might confuse the mentor with his antagonist, but as he understands what the mentor teaches him, he also understands that the mentor only put him through whatever he put him through so that he might learn. (And yes, to complicate things further, of course the mentor can be the antagonist, or the friend can turn out to be the enemy, or whatever you want. Stories can be a lot less schematic than writing teachers make them out to be, so, as final advice, don't worry about who or what the reflection character is but write your story.)