If you can't give me an argument as to why all your axioms apply, then why should I accept any of your claims?

I see no counterexamples to any of the axioms. If they're so wrong, you should be able to come up with a set of preferences that someone could actually support.

A specific form of preference that violates the axioms? Any preference which is "irrational" under those axioms, and you already acknowledged preferences of that sort existed.

You need to argue that those are useful in some sense. Preferring A over B and B over A doesn't follow the axioms, but I see no reason to use such systems. Is that really your position, that coherence and consistency don't matter?

Any preference which is "irrational" under those axioms, and you already acknowledged preferences of that sort existed.

As an extremely basic example: I could prefer chocolate ice cream over vanilla ice cream, and prefer vanilla ice cream over pistachio ice cream. Under the Von Neumann-Morgenstein axioms, however, I cannot then prefer pistachio to chocolate because that would violate the transitivity axiom. You are correct that there is probably someone out there who holds all three preferences simultaneously. I would call such a person "irrational". Wouldn't you?