When trying to make a case for some position or idea, we frequently encounter questions which challenge the coherency or validity of that position. When we are able to adequately answer those questions, our position becomes stronger. When we cannot answer the questions, then our position is weaker. If, however, we avoid the question altogether, then our reasoning process itself is revealed as possibly weak.
It is unfortunately common that many important questions and challenges go unanswered but why do people do this? There are surely many reasons, but a common one may be a desire to avoid admitting that they might be wrong. They might not have a good answer, and while I dont know is certainly acceptable, it may represent an unacceptable admission of at least potential error.
Another possible reason is that answering the question might lead one to the realization that their position isnt valid, but that position plays an important role in their self-image. For example, someones ego might be dependent upon the premise that some other group is inferior to them in such a situation, the person might be strongly inclined not to directly answer questions about the justification of that alleged inferiority, otherwise they might have to acknowledge that they arent so superior after all.
Not every instance where a person seems to be avoiding the question qualifies as such sometimes a person may think that they answered it earlier or at another point in the process. Sometimes a genuine answer doesnt immediately look like an answer. Consider:
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Patient: Is my condition life threatening, doctor?
Doctor: Well need to do more tests before we can determine that.
In this example the doctor has told the patient that she doesnt know if his condition is life threatening, but she didnt say that outright. Thus, although it could appear as though she avoided the question, in reality she did give an answer perhaps one which she thought would be a bit more gentle. Contrast that with the following:
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Patient: Is my condition life threatening, doctor?
Doctor: Dont worry about that right now. You get some rest tonight and Ill be by tomorrow.
Here, the doctor has avoided answering the question entirely. There is no hint that the doctor still needs to do more work in order to arrive at an answer; instead, we get an evasion that sounds suspiciously like he doesnt want to face telling his patient that she might die.
When someone avoids direct and challenging questions, that does not justify concluding that their position is wrong; it is very possible that their position is 100% correct. Instead, what we can conclude is that the reasoning process which leads them to assert their position may be flawed. A strong reasoning process requires that one either have already dealt with or be capable of addressing important issues. This, of course, means being able to answer challenging questions.
Typically when a person avoids answering a question, that question was posed by another person in a debate or discussion. In such cases the person is not only evincing flawed reasoning, but also violating basic principles of discussion. If you are going to engage in a conversation with someone, you need to be willing to address their comments, concerns, and queries. If you dont, then its no longer a two-way exchange of information and views.
However, that isnt the only context in which a person might avoid answering questions. Its also possible to describe that as occurring even when a person is alone with his thoughts and considering a new idea. In such cases they will surely face a variety of questions they ask themselves, and they might avoid answering them for some of the reasons suggested above.

