the party setting forth a proposition has the burden of proving the merits of that proposition. in particularly esoteric cases involving complex matters, it is helpful to the overall support of your argument to set forth the parameters of the structural framework of that argument. Once the analytical framework is established, it would then be customary to demonstrate how the facts of a given case meet the criteria of that framework, thereby establishing the proof of the proposition.

In the present case, focusing narrowly on the issue of antitrust, that would require you to set forth the requirements of what it takes for an antitrust allegation to succeed. You would say "A plaintiff has to prove X, Y, and Z, while a defendent could say "A, B, and C to disprove the allegation." You would then say, "Given those factors, here is how BYU being excluded from a conference like that would meet the requirements of antitrust".

You didn't do any of that. You just said "You have to set criteria for exclusion. Since there's none that can justify the exclusion of BYU, its antitrust."

That is incorrect. You didn't even set forth what the criteria are for a successful antitrust violation. Based on the kinds of arguments you used, its pretty clear to me you don't actually know what a successful antitrust violation entails. It's a much more complex economic argument about price fixing and prior restraint on economic trade and monopoly power, not about whether a particular actor who doesn't benefit in a system is as good or better at plying their trade than other actors who benefit in the system.

you're asking me to prove a negative, which is of course impossible. But despite the fact that I can't do that, i did attempt to reason by analogy by demonstrating that the current P5 system--unfair as it is--doesn't violate antitrust, and that a similarly unfair new system would also not invoke antitrust violations. It may be unfair, but it doesn't violate a restraint on trade.