Vulnerability. It's something that martial arts teachers (anyone, really) are generally afraid to talk about.
And given the prevailing marketing line that consistent martial arts training will turn you into Wolverine (minus the adamantium skeleton….unless you train at the Weapon X Combatives Institute), I can understand the internal logic that gives birth to this fear: "If I'm vulnerable, my students will think I'm a shitty martial artist. If they think I'm a shitty martial artist, they'll quit and go somewhere else. I don't want my students to quit, therefore I cannot be vulnerable."
While potentially good for student enrollments and retention, this type of thinking goes against the central promise that many martial arts make to their communities of practice: freedom from fear. Being vulnerable does not go against the ethic of martial arts, but fulfills it. It makes you a better teaching, student, and general human being. It gives you the courage to face the fact that, whether it's the ability to fight, teach a certain technique, open and run a school etc. there's somebody out there that is better than you.
And you can either take that as an opportunity to improve yourself, or not.