The following is supposed to be a Game Theoretic take on the causes of human irrationality. Of course, being my own views and having been heavily influenced by what I have experienced and observed, they are liable to have many inherent biases built inside them and I do not think they are very correct.
Although in a game, a rational player would play the strategy that is expected to increase his payoff, altruistic people might not be amenable to such analyses because of the apparent disregard that they have for their own welfare (or self interest). I'd like to point out that 'altruistic' people can be included in the realm of rationality. This can be done by considering the fact that people, for whatever reason, may change the structure of the game (or perceive differently, the structure of the game) being played by assigning different numbers in the payoff matrix than what are supposed to exist objectively. Now it is possible that due to their philosophy of what they think is correct and right (as opposed to wrong), causes them to perceive their payoff matrices as different than what is perceived by other people. In this case, they are again maximising their payoffs as is expected of rational people by putting in a higher payoff on the strategies they ultimately end up playing.
Hence on the surface at least, I do not see a reason for a dichotomy.
The causes for the different payoff structure being assigned is what is discussed next.
In my opinion, the cause stems from the fact that the game being played is not Common Knowledge. The payoff structures are hidden somewhat and although (if the game is repeated) there can exist emerging patterns in the assignment of payoffs to different strategies by players, the fact that common knowledge does not exist causes the other players in the game to rely on their inbuilt, hardwired Bayesian Inference subroutines in their brains which inherently, are heavily dependent on the players' experiential domains.
This is, in fact the reason for superstitions. People seeing black cats crossing their path, relating it to previous mishaps in their own lives infer that the blame for some putative future accident rests solely on the puny shoulders of the cat. This is classic case of correlation being mistaken for causation.
Hence being denied common knowledge and public payoff functions, the game being played transforms dramatically into that in which guessing the behaviour of the adversary becomes a far more intractable problem of mathematics. Also, the prior programming of the individual by means of education (or the lack of it), experience, genetic hardwiring etc makes him prone to assess the game in a radically different way than is usually studied in formal discourses of Game Theory.
So perhaps the more meaningful question should not be "Why are humans irrational?" but "How are humans irrational?"