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?