As I said, that definition of "arrogant" is only common usage. It is not the original meaning of the word. And having such a difference, the conclusion will obviously differ.

In the case of Hikari, he knew that he was going to beat her, and simply stated that she may embarass herself (which she did) if she continued her challenge. It is of course in consideration of his skill in wrestling, and not an overestimation or excess of belief in oneself.

If you take arrogant to mean that way, even I agree that Kei is arrogant. And if you take arrogant the way I understand it (as well as how it is defined in most if not all vocabulary sources) then even you have to agree with my statements. There really is no argument, at least not anymore.