How do you deal with peers (instructors or trainers) who have no humility?

Try to ignore them if you can. Just be your own pleasant self and keep as much distance as you can. You only have to deal with them for a few hours a day (if that much) but they have to live with themselves for the rest of their lives.

One thing I would avoid: don’t talk negatively about them to anybody. If other people solicit your input, do not engage in a bashing in absentiam. I like to follow that rule that if you have nothing positive to say, say nothing at all.