I think your post can be boiled down to simply, "If you always win arguments, you are collecting errors."
This part isn't true.
Perhaps. My experience was similar to yours in many respects, but very early on it became clear to me that I was a member of a very small club. We were subject to standardized testing starting in, I believe, third grade, and were delivered results that compared us to hundreds of thousands of other kids across the country. It is hard not to feel "gifted" when you are given a very officious looking document with a government letterhead and the number "99" on it (the primary metric of academic achievement was a percentile score from 1-99) every three years. What further set me apart was the honour of being the only atheist and sceptic in a religious elementary and secondary school. Perhaps I presumed myself intelligent only by virtue of the bottomless lack of rationality I was surrounded by. Overcoming Bias would have been exceptionally welcome in those days.
"Because giftedness is not to be talked about, no one tells high-IQ children explicitly, forcefully and repeatedly that their intellectual talent is a gift. That they are not superior human beings, but lucky ones. That the gift brings with it obligations to be worthy of it."
Thankfully. High-IQ children know they are high-IQ; if they can't figure out how smart they are, they aren't very smart. They don't need to be told they're special, though. We need people who live intelligently rather than live for the purpose of being intelligent.
Telling an intelligent person they are obliged to use their intelligence in service to others is the quickest way of convincing him or her not to.
Apparently, most people who are vegetarians don't necessarily believe that it's not okay to slaughter other animals for consumption.
That's quite true. Most vegetarians have adopted their eating habits out of health related, not ethical, reasons. Those with ethical concerns are "vegans", and their diets usually go beyond vegetarian restrictions. This, of course, is a gross generalization.
I think I'd consider the eponymous hero of Stephen R. Donaldson's Chronicles of Thomas Covenant a rationalist character - at least in the first book, Lord Foul's Bane. Covenant is struck by a car and wakes up in a fantasy world. Accordingly, he refuses to believe it is real, and most of his decisions stem from that, including a rather horrible one that has far-reaching consequences throughout the first series. What compounds the whole situation is his debilitating leprosy. Donaldson created a very plausible depiction of a real person stranded in a fantastic world, and while Covenant is not entirely rational, he does live by a very strict methodology.
Isaac Asimov was also one for creating rational heroes, but much of his work is quite dated (and his female characters often leave much to be desired). Hari Seldon is a pleasantly rational character, though. The ultimate author of rational heroes is Ayn Rand, of course, but her characters are, as you say, about being rational.
I don't have an argument here; rather, I just want to see if I understand each position taken in the dialogue. After all, it would be a dreadful waste of time to argue one way or the other against our three musketeers while completely misunderstanding some key point. As far as I can tell, these are the essential arguments being made:
Yancy's position: that fairness is a rational (mathematical) system. There is no moral factor; rather than "to each according to his need," it is "to each according to the equation." This presumes fairness is a universal, natural system which people must follow, uncomplaining; any corruption of the system would be unfair, any bending or breaking of the rules renders them useless.
Zaire's position, that it is fair for individuals to define the product of fairness, handily illustrates this; his conception of fairness breaks down as soon as another conception is introduced. Fairness is entirely relative.
Xannon's initial position is that the product of fairness can be rationally derived from individually relative definitions of fairness; that fairness itself is the sum of differing concepts of fair.
Xannon revises this position, in that fairness is derived from the moral rights of a group and has an intrinsic, understood value. Those who do not inherently comprehend this value are not moral and do not belong to the group, like the murderer. Of course, this assumed that passersby, like Xannon, would side with the victim. Not only could they side with the assailant, they could even refuse to become involved. If the victim is "licensed" to resist being murdered, is the victim likewise licensed to kill the murderer in self-defense, and is that fair? The question of "who started it?" begins a new problem. If the observer is joined by five others who think that the victim, who killed his attacker in self-defense, must be put to death, is that also fair? This position argues for the existence of absolute morality, but only achieves a weak implication of moral relativity.
This is at odds with Xannon's initial position; if Zaire wants more of the pie than Yancy, but Xannon sides with Yancy, Xannon thinks it is fair to average their desires. However, Xannon would not average the desire of the murderer, the victim, and the passerby. If the murderer is presumed in the wrong, then Zaire is also presumed in the wrong. Therefore, it is unfair to attempt to combine Zaire's desire with Yancy and Xannon's.
In essence, Xannon's position is ultimately not far removed from Zaire's; where Zaire believes in the individual's right to define fairness, Xannon believes in the group's right to the same. Both believe in a moral right to inflict their own definition of fairness on the other. Yancy, in believing a universal system of fairness can be applied, would attempt the same. Further, even if Xannon agreed Yancy's proposal was fair, it would not be for the same reason, as Xannon believes fairness is derived from moral right; therefore, arriving at a fair decision through the amoral application of a rational system may not be "morally fair" to Xannon. There is no resolution to be found here.
I would like to see the question of the purpose of fairness addressed more comprehensively. If fairness as a system is not effective, why does it exist? If it is an artificial social construction, it must have a agreed-upon definition; if it is an evolved, biological system, it must have a physical basis; if it is a universal rule, there must be evidence of it.
"Or you're always choosing the right side."
The problem is that if you ever win an argument when you are wrong, subsequent arguments with anyone who has accepted your false conclusion leads to further errors. Furthermore, to avoid this, it is not enough to always choose the right side. You must be right about everything you convince your opponent of. Even the right conclusion can be supported by false evidence. Lastly, you will probably engage in arguments that have no right side or conclusion. Such arguments should not be won or lost - rather, both sides should admit when there is insufficient evidence to support either case.
Of course, you could always choose the right side, one hundred percent of the time, every time. How likely is that compared to the likelihood of being argumentatively superior, though? Having a compelling enough argument to convince someone else of a false conclusion means having a compelling enough argument to convince yourself of the same thing.
I could be wrong about this, though :)