... shows that you don't have to be an atheist to make great discoveries.
I don't think anyone is making the argument that you do. Plenty of people get through life without basic rationality, and some even do interesting and amazing things. That's not an argument for being religious though - at best, it shows that in certain cases religion doesn't completely cripple your rationality. It's still a risk, however.
As for religious people being happier than atheists, ... In my experience, the average atheist is not at the basic level talked about in this post. Slightly more rational than the average theist I've met (and I tend to more time around the smarter, more rationalizing type of theist), but still not even close to this.
Obviously that's just anecdotal, so I wouldn't bet much on it at all, but it's enough for me to question the validity of applying murky evidence about happiness and religion to a discussion about teaching basic rationality. If anything, I would say that evidence seems to more strongly indicate that we should teach basic rationality, because leaving religion without it might make it more difficult to be happy.
To paraphrase the Black Belt Bayesian: Behind every exciting, dramatic failure, there is a more important story about a larger and less dramatic failure that made the first failure possible.
If every trace of religion was magically eliminated from the world tomorrow, then—however much improved the lives of many people would be—we would not even have come close to solving the larger failures of sanity that made religion possible in the first place.
We have good cause to spend some of our efforts on trying to eliminate religion directly, because it is a direct problem. But religion also serves the function of an asphyxiated canary in a coal mine—religion is a sign, a symptom, of larger problems that don't go away just because someone loses their religion.
Consider this thought experiment—what could you teach people that is not directly about religion, which is true and useful as a general method of rationality, which would cause them to lose their religions? In fact—imagine that we're going to go and survey all your students five years later, and see how many of them have lost their religions compared to a control group; if you make the slightest move at fighting religion directly, you will invalidate the experiment. You may not make a single mention of religion or any religious belief in your classroom, you may not even hint at it in any obvious way. All your examples must center about real-world cases that have nothing to do with religion.
If you can't fight religion directly, what do you teach that raises the general waterline of sanity to the point that religion goes underwater?
Here are some such topics I've already covered—not avoiding all mention of religion, but it could be done:
But to look at it another way—
Suppose we have a scientist who's still religious, either full-blown scriptural-religion, or in the sense of tossing around vague casual endorsements of "spirituality".
We now know this person is not applying any technical, explicit understanding of...
When you consider it—these are all rather basic matters of study, as such things go. A quick introduction to all of them (well, except naturalistic metaethics) would be... a four-credit undergraduate course with no prerequisites?
But there are Nobel laureates who haven't taken that course! Richard Smalley if you're looking for a cheap shot, or Robert Aumann if you're looking for a scary shot.
And they can't be isolated exceptions. If all of their professional compatriots had taken that course, then Smalley or Aumann would either have been corrected (as their colleagues kindly took them aside and explained the bare fundamentals) or else regarded with too much pity and concern to win a Nobel Prize. Could you—realistically speaking, regardless of fairness—win a Nobel while advocating the existence of Santa Claus?
That's what the dead canary, religion, is telling us: that the general sanity waterline is currently really ridiculously low. Even in the highest halls of science.
If we throw out that dead and rotting canary, then our mine may stink a bit less, but the sanity waterline may not rise much higher.
This is not to criticize the neo-atheist movement. The harm done by religion is clear and present danger, or rather, current and ongoing disaster. Fighting religion's directly harmful effects takes precedence over its use as a canary or experimental indicator. But even if Dawkins, and Dennett, and Harris, and Hitchens should somehow win utterly and absolutely to the last corner of the human sphere, the real work of rationalists will be only just beginning.