I'm trying to listen to both sides of this issue to get a better understanding. If this question could be better worded to be more helpful, please help me out.
First: the opinion which it is attempted to suppress by authority may possibly be true. Those who desire to suppress it, of course deny its truth; but they are not infallible. They have no authority to decide the question for all mankind, and exclude every other person from the means of judging. To refuse a hearing to an opinion, because they are sure that it is false, is to assume that their certainty is the same thing as absolute certainty. All silencing of discussion is an assumption of infallibility. Its condemnation may be allowed to rest on this common argument, not the worse for being common.
(with many arguments continuing).
The argument in Chapter 2 has been summarised as:
In Chapter 2, Mill turns to the issue of whether people, either through their government or on their own, should be allowed to coerce or limit anyone else's expression of opinion. Mill emphatically says that such actions are illegitimate. Even if only one person held a particular opinion, mankind would not be justified in silencing him. Silencing these opinions, Mill says, is wrong because it robs "the human race, posterity as well as the existing generation." In particular, it robs those who disagree with these silenced opinions.
Mill then turns to the reasons why humanity is hurt by silencing opinions. His first argument is that the suppressed opinion may be true. He writes that since human beings are not infallible, they have no authority to decide an issue for all people, and to keep others from coming up with their own judgments. Mill asserts that the reason why liberty of opinion is so often in danger is that in practice people tend to be confident in their own rightness, and excluding that, in the infallibility of the world they come in contact with. Mill contends that such confidence is not justified, and that all people are hurt by silencing potentially true ideas.
Keeping all these assumptions in mind, it appears the proponents of no-platforming are going against what John Stuart Mill intended. He reasons that we need to be able to hear 'dangerous ideas'. (Because as John Stuart Mill argued, these ideas might be right).
The question behind my question is "Why can't people just listen to each other?" but I'll stick to one clear question.
My question is: How do New Left proponents of No Platforming answer John Stuart Mill's claim that all silencing of discussion is an assumption of infallibility?