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The optimal play and the "rational" play are two different things. I've already stated that I would be very unlikely to offer a low offer to my opponent, mainly because I figure he'll be an idiot and overvalue spite.

[Emphasis mine]
Your terminology suggests you're seeing this as a game that you play to maximize your score. The very title of the thread supports that framing. If that was in the "social contract" of the interaction (as it is in a game of poker) then going cutthroat would be protected from social stigmas by the "magic circle" of the game (just like in poker you can deceive and bluff, in Diplomacy you can stab, or in boxing you can punch, with ideally no hard feelings). I was intending this more as a metaphor for social interactions in the wild.

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What morally wrong act has the splitter committed in the original case?

Both players have equal claim (or lack thereof) on the money. There's no moral basis for anything but an even split, which is just a sane and socially ingrained default. As he deviates from an even split, the splitter not only gets utility at the boolean's expense, but he causes more harm than value he gets (because of the added grief of abuse). By increasing the risk of a veto, this disequilibrium further reduces the global expected value.

You may contest that there are "irrational" forces at play here, like the expectation of an equal return as the basis of what is "fair" in absence of other claims, and the drive to punish exploitive behavior. The conviction with which you call these irrational and idiotic suggests that you hold a reductionistic belief that game theory is straightforwardly applicable to (even stylized) real life interactions, despite assumptions like unbounded "rationality" on all parts, perfect information, perfect selfishness of actors, constrained time domain, isolated strategy space.

Don't you acknowledge the possibility that these "irrational" assumptions and biases may be evolutionarily stable, advantageous features for individuals and societies?

You do acknowledge that if you were the splitter, you'd be more generous than you think you "should", in anticipation for "idiocy". Of course, it's the prevalence of such actual "idiocy" that makes it a credible threat. And that, in turn, gets "idiots" a better payoff in this game. So isn't this "smart", in a way?

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