Students will have questions. Of course, that is an essential part of being a student. As the matter of fact, instructors will have questions, too! One may even argue that as long as you train, you will be looking for answers to one question or another. But, not all questions or answers are created equal!
The point here is not in the "dumb" questions people ask every once in a while, because hey don't know any better or are too lazy to just think about it it, or try it on their own. As an instructor there are two particularly challenging situations you are probable to experience sooner or alter in your work, regarding answering your trainees' requests.
The first is when they have a questions, but you don't have an answer. In itself, that is not unusual, we all have seen experts in various fields being in a similar position here and there. However, younger and fresh instructors are often stressed by this and tempted to come up with an ad hoc solution, to save their face. Here and there, depending on the person asking and the nature of the inquiry, such approach may work, especially if the teacher is skilled with words. It is OK, if the predicament pushes you to actually look into subject afterwards to see how to deal with the same question if it pops up again. Then again, if you are lazy or don't care about students' questions (in which case you shouldn't be an instructor) it could look like an easy way out and lead to complacency...in which case you are setting yourself for the other scenario. You get the question and try to wing it, but the answer is unsatisfactory and they let you know it. Now, this IS embarrassing, especially if you don't know how to handle it.
My experience though, as a long time martial arts instructor and school teacher, says it is far better to be honest about it. Say you don't know the answer, but promise to have it by the next training session. Moreover, make it a challenge for everybody in the class, and then spend the portion of the next meet in offering/comparing the solutions. BUT - make sure to do your homework! Others may or may not accept the challenge and seek the answers, but you have to. It will show those training with you that you are an honest and thoughtful instructor who really cares about their needs and do everything you do in their best interest.
The second situation is probably even more delicate, and something that grand majority of instructors, unfortunately, had to deal with somewhere along their path. There is this kind of student, usually the one who ask most questions anyway, while also being the biggest slacker when actually training. Typically, he or she will approach you with a question, maybe even a good and important one, and when you gladly answer it - it is not the answer they were hoping for. All your great arguments, brilliant reasoning, host of evidence and concrete hands-on demonstration will be futile. Such people have predetermined outcomes in their minds, and as far as they are concerned - you are wrong! By the way, this occurrence is more typical of seminars than regular classes.
Well, what do you do then? I am afraid the answer is - it depends. You maybe dealing with an otherwise nice and pleasant person who doesn't present any harm to the atmosphere in the group or detriment to the quality of the overall training. If so, ask to hear their opinion (and reasoning, if available), kindly nod your head and say you'll give it some thought. Usually that dissolves the situation and everybody can proceed with their work.
On the other hand, should you have on your hands a person who keeps pestering you with incessant questions and disputing everything you say or do, there is no choice but to drop them from the group. Again, depending on the context, it can be done politely or harshly. If it is a group situation at all, I would suggest that the person at hand cannot be best served in such environment and offer to give them private lessons. And if it is a private client in the first place...well, maybe the money is good enough to put up with their act, but I would probably say it is evident I wasn't the best instructor for their needs, probably just holding their progress back, and strongly suggest they look for training elsewhere.
Oh, and if you are a student!? Please, please, please!!! Be mindful of what are you asking and why, i.e. what are you trying to gain from the answer. If looking for a sincere response from the instructor, then take it and give it at least some thought and/or practice with the advice, before asking for clarification or voicing your dissatisfaction with it, should that be the case. Sure, if you are paying for the instruction, you deserve the best effort from the instructor. He or she may or may not be what you are looking for, and that's fine, but it doesn't give you the right to harass them. They may not be aware of their shortcomings, maybe being erroneous in the best of intentions, so it would be better to present your concerns in a one-on-one conversation first. And if it just doesn't work...walk away, don't waste your time and money in a place that makes you frustrated while failing to offer anything worthwhile in return. In any case, the conflict shouldn't be about who is right, but rather about what it the right thing to do.