Ours is not to reason why
To expand on the point about the difference between checking the world and not checking the world – to repeat –
Science has to check itself against the way the world is, and religion doesn’t. Science is about what is there whether humans can figure it out or not, and religion isn’t. (It claims to be, but it isn’t.)
What you get with an institution that doesn’t require itself to check against the world, is authority. You get the fiat, the Bull, the decree, the encyclical, the Index, the excommunication, the anathema, the charge of blasphemy or apostasy. You get the arbitrary.
Science has to show its work, and religion doesn’t.
This difference certainly doesn’t cash out as the first always making everyone happier and the second never doing so. On the contrary. But it does cash out as accountability in the first case and no accountability in the second. It is the difference between reasons on the one hand and arbitrary authority on the other.