The development of religious beliefs is most likely due to the evolutionary benefit of assigning agency to unknown causes. The famous example, which you are probably aware of, is that of the caveman sitting under a tree when he hears a rustling in the grass. If he assumes it is the wind and he stays seated, and it turns out to be a tiger, he will get eaten and will not pass on his genes. If he assumes it is a tiger, and he rushes to climb up the tree, he will be able to pass on his genes, even if it was really just the wind. Later, the early humans could cognitively connect the assumption of agency to to other causes, like the movement of the sun or the moon, and later to more sophisticated forms of religion.
That the root of religion served as an evolutionary benefit does not mean that religion and superstition serve a purpose now. In fact, I'd argue that any belief which detaches us from reality is potentially harmful - if not on an individual level, then on a societal level.
I suspect it's quite a bit deeper than that - religion helps to build group identities that enable members of a group to be more willing to assist each other. Humans are almost powerless outside of a group but extremely powerful within one; looking out for and setting up relationships of mutual assistance even with unrelated people is crucial for individual survival along with that of the group. It is also intimately tied up with most aspects of pre-modern culture. My guess is that if you strip out the religion and the superstition, premodern humans lose a lot of the drive to do things beyond simple survival and reproduction. It seems likely to me that this is partly true for modern humans as well.
In particular, myth is hugely important across all pre-modern cultures. That's a pretty strong clue to me that a world where everyone thinks totally rationally would be one where humans have cut out one of their most important tools of communication. I suspect that actual belief in myths helps to keep them alive and shaping culture. Keeping in mind that human minds have not changed in the past few centuries, I tend to be very skeptical that any attempt to strip out some human cultural universal is ever going to succeed, or that it would be desirable in the first place. The architecture of the mind is fundamentally non-rational.
Virtually every religious claim that was ever made has been refuted. We may never be able to completely refute the most vague, deistic notion of some kind of creating force, but that is not what religious people tend to believe in anyway.
Right - most are not falsifiable at all, and where they make claims that can be tested, they fall apart or at best come back inconclusive. No argument with that.
Individual happiness is a poor indicator for the usefulness (or harmfulness) of religion. To take an extreme example, wiretapings of Muslim suicide bombers have shown that before they blow themselves up they are extremely happy, because they believe that they and their whole families will go to the highest level of heaven. Needless to say, their actions are not conducive to human flourishing, neither for themselves nor for others.
You seem to arguing for a kind of placebo effect of religion. But it seems to me that if the benefits that religion offer are not based in reality, there should be no reason why we can't build a society that offers the same benefits. When it comes to spirituality, religion, by having the monopoly on the spiritual realm, is actually impeding progress which could come from scientific research on what our brain is capable of experiencing. This is a point Harris makes in the book I mentioned.
To a great extent I am, but here the placebo is the treatment. I hope that the specific nonsense beliefs can be divorced from religion and still have the useful part of religion remain, but I'm skeptical that it can be done with the same level of success.
Being religious appears to be positively correlated with self-reported happiness in the majority, maybe the vast majority, of studies done on it. There are a few that find no significant relation, as there always are in social science, and I can't find anything that has a negative correlation. It is of course possible that the main factors in the happiness increase are the social gatherings and support networks that come with organized religion, but this would go back to my hypothesis that this is one of the biggest positive functions of religion in general. Religious people seem to find motivation and fulfillment in being individually religious as well, though.
You say that individual happiness is not necessarily helpful for society, which is true - euphoric suicide bombers are definitely a net negative. But what I'm talking about is an effect that seems to make most individuals happier on net, and to increase their social connections as well. This is unambiguously good, and it would be hard to argue at least from a utilitarian perspective. If neuroscientists can come up with some advanced way to get the same or more benefit, as it seems like Harris (sort of) suggests, I'm all in favor of that.
I'm not sure to what extent the myths along with patent nonsense can be divorced from the religion without weakening the social and psychological benefits of religion. There certainly are organizations like the Unitarian Universalists, along with a few strains of Hinduism and Buddhism, that work for some people in providing spiritual and social connection without involving the supernatural. None, though, seem to be particularly common, and the overall experience of increasing secularism in the Western world indicates that most people just leave religion without trying to replace it with something. And, perversely, some of the most preposterous faiths like Mormonism do especially well on surveys of happiness and social connection.
Harris' main argument is that we can speak about morality in objective terms. He doesn't claim that liberalism and secular humanism is necessarily the best we have, but that they are clearly better than most other moral systems mankind has experienced, since they are most conducive to human flourishing. His metaphor of a moral landscape, which potentially has many peaks (and many valleys), suggests that various different systems could be equally benefical.
Harris and the other individuals you mentioned are more like yourself than you think.

By the way, if you don't believe in the existence of God, you are an atheist. Being an atheist just means you haven't been convinced by the evidence for God, not that you can say for certain a God doesn't exist (which nobody really can).
Yeah, The Moral Landscape is the book of his I read. I did like the landscape metaphor, especially because I think in terms of mathematical functions anyway, and I imagined something like the way a chemical system tries to find equilibrium by "exploring" the free energy of different available configurations until, if it has enough energy, it settles into an energy minimum. I do agree that morality isn't totally relative - there are things that nearly all humans across cultures will agree on. It clearly has crucial roles in keeping people in a society cooperating with each other and not cheating by trying to doing things that benefit the individual at the expense of the group.
I appreciate that he thinks that other possible social orders might be even better, but I do take some issue with the idea that liberalism and secular humanism are the most conducive to human flourishing. I don't know what that is supposed to mean. I also don't think there's a good way to measure human satisfaction or flourishing or anything of the sort, and I suspect that if such a thing were invented, all you would end up with is a form of utilitarianism. Now I'm sort of on board with utilitarianism - I'm making utilitarian arguments for religion, for instance. But I don't think he is. If we were to determine that the social order that leads to the most fulfillment was religious fundamentalism, or if we were to figure out that most women really feel more fulfilled staying home and taking care of children, should we structure our morality accordingly? I never felt he adequately addressed that sort of objection.
I got the book you recommended though and I'm looking forward to reading it. It's quite possible I underestimated his open-mindedness. As for atheism, I'm definitely an atheist by a loose definition. I tend to avoid that label because using it always causes people to think that I believe there is no god, and 7 pages of irrelevant argument about the meaning of "atheist" ensue. Agnostic seems to fit better overall. But both labels are correct and not mutually exclusive.
edit: Wow, that's a fully Funky-sized post.
