“It is better to correct them after class, rather than during. This shows respect. If you challenge a teacher while they are teaching, and I learned this the hard way, you may come across as undermining them and this will lead to them resenting you.”
Then they are simply teachers, not masters. Otherwise, it is the very function of a master to assist oneself in functioning out of ones own intelligence. That includes even having doubt towards the master himself. If you are just, perhaps out of admiration, or fascination, or just simple gullibility - accepting everything that the master is saying, then it is only going to strengthen your conditioning and dull your intelligence.
Nothing should be accepted without question, and if there is a burning and sincere desire to learn, with a deep receptivity - then no formalities whatsoever are needed in a direct encounter between master and disciple. That is when the situation becomes alive, with a transmission which is fresh and spontaneous. Only one who has enough courage to set all formalities aside is capable of facing a master - who is going to do whatever is necessary, regardless of ones likes and dislikes, to assist you towards your liberation. If the disciple has a desire to “correct” the master or disagree with him, if it is truly out of a desire to seek the Truth, then rather than becoming upset, on the contrary he will feel enormous gratitude for such a sincere spirit of inquiry. Because to come across somebody who truly has ones own questions, who has awakened the thirst of seeking, is a rare quality which needs to be nurtured.
But, if one is simply being argumentative for the sake of ones own egoistic entertainment, then that is an entirely different matter. Such students should not be tolerated, and in the first place they should not have been accepted as students. The Way is not a childs play, and only those who are willing to leap off the edge of a mountain and into an bottomless abyss, even come to know of the freedom which is theirs from first to last.