Watch his first meeting with Hikari again if you want to see whether he has a tendency to show arrogance towards people in general. You can't say his arrogance is only reserved for Hikari when he was like that even before he had met her. Unless you suggest his personality suddenly changed the second he saw her. He's just not a flamboyantly arrogant but more silently arrogant. It's conceivable that whole aspect of personality developed as a self-defense mechanism if he has always been the best. Such people have to suffer the jealousy and envy of others throughout their lives and under such circumstances they can only either submit or ignore others (which can be observed as arrogance) (well, I suppose beating the hell out of others to make them submit is also an option but I choose to disregard that choice here).

Like has been said, arrogance is a negative description, and as such it surely can be said to be overly prideful of one's worth. I have to agree with Ryllharu on that; it doesn't matter whether the difference of worth is real or not, it only matters the arrogant person acts like there is a difference. That's why you can have situations like in this ep, where Hikari was starting to submit to the three jerks (being not arrogant) and Kei, on the other hand, chose to ignore them, displaying arrogance (as observed by those three).