When the teacher is giving a speech, and he/she says something that's wrong in your opinion, it's the best not to interrupt, since she might not be the one that's wrong. Imagine, you rais up your hand and point out that the teacher is wrong, but in fact, he/she isn't， and corrected you, that will be really awkward. first, you're interrupting the class and also interrupting other student's learning progress. second, other students will be laughing due to your funny mistake. Or, the teacher is actually wrong, and you pointed out his/her mistake and corrected it, that would be helpful, but that won't happen usually. That's why the right choice is to ask the teacher when the class ends and everyone has already left and the teacher is packing up and about to leave. If you say nothing, your opinion won't be expressed openly, and maybe the teacher is wrong, and the teacher never realizes it and the whole class will have a wrong understanding of the question, so expressing your opinion is important and expressing it in a right way is even more important.
      In different situation, for example, during a meeting. The speaker is your boss, and he made a mistake. It's the best to not to say anything. Because, If you interrupted him/her, and is he/she is actually wrong, your boss would be really angry and embarrassed if he/she really cares about how other looks are him/her, and you may even get into serious trouble if the boss is angry enough. If you're the one who is wrong, the boss would be even angrier because you interrupted his/her speech for nothing and you wasted everyone's time. and your boss may need you extend the meeting the time and he would probably miss something important and you might even lose your job for this.