What if someone is an arrogant S?
I'd say it looks like you're inferencing that I actually think Ns are more capable of arrogance than Ss. I don't. But I do think Ns dominate this forum, and that so many of them believe that N is automatically more intelligent than S that there is a climate of superiority. If for no other reason than the Ns totally overwhelming the Ss in number here, there is a definite overwhelming sense that Ns dominate Ss in intelligence as well, perhaps as much as it is believed Ss dominate Ns in number in the "real world."
People want to be intelligent and worthwhile, S, N, black, white, tall, short, ugly or beautiful. People have a hard time reconciling their need to maintain their self-esteem with their need to see themselves objectively. That's probably the source of arrogance in every shape and form.
Finally and more importantly, all types use all functions (HELL0!).
I think that's a good point. We all have thinking, feeling, sensing and intuition in our top four functions, without exception. If N is more intelligent than S, then it would follow that the types that lead with N would be the most intelligent: ENxP and INxJ.
Still, there is the popular belief running around that INs are usually the most intelligent and the most likely holders of the highest and most impressive IQs. That contradicts the axiom that people who lead with intuition are the most intelligent, because it cuts out ENxPs.
Also, INTPs are often regarded by many as the most intelligent type, but their sensing function is, according to function order theory, more accessible to them than any INxJ's.
There are a few popular theories running around, none of which I place stock in. People are remarkable. We all have the same eight functions, and we all have S, N, T and F in our top four, in different orders. We're capable of being both amazingly similar and breathtakingly different. I truly believe S and N have nothing to do with intelligence, adaptiveness, capableness, etc, etc.