I myself cannot detect arrogance in others, but as far as I understand it:
If you talk to a person about one of that person's shortcomings that you don't have, and that person cares about it, you are perceived as being arrogant.
For example: if a rich person says to a poor person "Ah... if only you could at least pay your bills, you would be able to buy that awesome computer that I have", that will probably be perceived by the poor person as arrogant.
This probably isn't an all-encompassing rule, but that's how I see it.
EDIT: Come to think of it, a better rule could be: If a person knows/thinks that you are deliberately invoking envy in him, either explicitly or implicitly, he will detect that you are arrogant.
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"The aim of the wise is not to secure pleasure, but to avoid pain." -Aristotle