There are two possible views that you can hold about your answer to a question (or just one depending how you look at it). First, you could think that a particular answer is true. And second, you could think that you don't have an answer because the possible answers you have thought of are clearly wrong. But in the end you only have an answer if you think that you are right.
Why then do people insist on accusing others of arrogance for having an answer and thinking that their answer is correct. Its a necessary presupposition of claiming to have an answer: you think that your answer is correct, or you wouldn't have an answer.
If this is not the heart of the accusation then I think accusation is that the questioner has categorized their question in the realm of unanswerable and they are offended that someone could claim that it is answerable. Instead, the productive question would be to ask whether a particular question is answerable. Then they can voice their belief that the question is not answerable and give evidence of why they hold this belief and hopefully a productive discussion can result.
There is no arrogance in and of itself in having an answer to a question or thinking that you are right - it is the logical prerequisite of having anything meaningful to say.
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