But this argument is itself even more incoherent on its own terms. If subjectivity is the foil that makes the "possibility of being wrong" a poor argument, it also makes every argument a poor argument. Any epistemology that treads anywhere close to that ends up indistinguishable from nihilism.

Regardless, Bilgrami is not here arguing against Mill. Not remotely! I don't know, having not heard Bilgrami's arguments, whether the error is yours or his. But Mill does not argue for balance. I've misplaced my copy of On Liberty, so I won't provide a quote right now, but Mill consistently argues for freedom and for successive improvement of ideas, not for implementing it via enforced "balance" requirements (which are unlikely to achieve that end anyway).

Balance, in the form of the Fairness Doctrine in the U.S., was an attempt to introduce opposing viewpoints to broadcast media in the 1950s, after people noted that when one has a really big megaphone--as broadcast services did--then one can drown out any contrary speech rather effectively, thus distorting the "marketplace of ideas" (Mill's idea). It was never part of Mill's conception, but rather a means to try to ameliorate a technologically-induced problem that Mill didn't have to account for.

Arguing against balance isn't, however, arguing against Mill for the simple reason that he didn't advocate for it. He was an intellectual libertarian in that regard, envisioning a free "marketplace of ideas". Of course, that is where we might criticize his ideas as incomplete, because there are a bunch of market distortions that are possible in intellectual as well as physical markets.

Nonetheless, you make an extremely weird case against balance: "The call for balance is also a means of silencing dissident voices and marginalizing non-majoritarian views."

This is the polar opposite of what happens when balance is actually valued. When balance is advocated for, you invite the dissident, non-majoritarian voices to balance the establishment voice.

It's only once the supposedly "non-majoritarian" voices take over to the exclusion of alternative viewpoints that balance would push back.

Practically any rule, no matter how advisable, can be corrupted by selective application against one side of a matter or against select groups.

If we have a law against murder, and we were to lock up Palestinians for murdering Jews, but not Jews for murdering Palestinians, the problem would not be that there's a law against murder. The law is fine. It's the application that is the problem.

So your critique seems doubly misguided.

Firstly, you frame the critique as one of Mill, but don't talk about Mill's ideas.

Secondly, you criticize balance using examples which would be made better by an actual embrace of balance.

There is one point where you and/or Bilgrami (again, I can't tell how much is you and how much is him) might collide with Mill, which is the contention that, "Her responsibility as a teacher is to communicate those conclusions — and the point of view that informs them — as effectively as possible, not to seek to represent all sides and all points of view."

This is rather contrary to the goal of having a precise understanding of (an approximation of) the truth via collision with alternative ideas and arguments.

So here we have to ask: why favor one versus the other? You/Bilgrami advocate for students to be given the answers from a point of view; Mill, one imagines, would advocate for students to be taught the argumentation--which could certainly lean towards the conclusions but wouldn't skip putting the best face on opposing ideas in contentious areas.

Now, given how pro-liberty Mill was, I presume he'd permit the type of answer-heavy one-sided perspective that you advocate. But in this one area where you and Mill actually seem to have a disagreement, his (putative) perspective seems far better for supporting an informed populace.