Natural horsemanship: Just because you 'work with the horse' doesn't mean other training techniques won't work, and doesn't mean all your techniques will work every time.
Bitless people: not all bits are evil, not all horses can go bitless. Not all people use bits to cover up holes in training.
Bit people: Some horses would go better bitless, and some can only go bitless.
(bad) Big name trainers: Who cares how many horses you've trained? If you screw up, you screw up.
To all students (and trainers) out there: Don't get too hung up on labels. Appraise each aspect or technique on it's own. You might skip over something that could really help you.
To all trainers: Don't be offended if your student wants to see other trainers in action. It is unfair to expect them to only listen to you and become a carbon copy of you.
I had more, about breeds and showing, but this post is long enough. What topic bothers you the most?