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Are you not a layman? I'm merely an engineer - technical but not a scientist. I am however well aware that vast amounts of what we think we know are just reasonable, mostly-working, hypothesis.
If you're an engineer then you're more aware than most. The reality is that everything we know are various levels of hypotheses. Those that are the best working hypotheses in their field are called theories, but every single one that I'm aware of has areas in which it's incomplete.
Take electromagnetism and gravity, which between them account for basically everything that happens on a human scale. Both are pretty well defined at the sort of engineering level that you might need to make a bridge or a computer or bake a loaf of bread, but at the cutting edge of the fields there's so much left to be learned.
Even at low levels there can be surprising areas that lack knowledge simply because no one has gotten around to doing the work. I'm sure you've come across some.
No, a belief is what someone thinks to be true without any proof. They may well have a reason for it. The reasoning may be flawed, but that takes nothing away from the end result - someone has a belief. Let's say they're unwilling to change their view based on new information (present tense). That does not mean they won't change their view (in the future) based on new information.
Say there's a bunch of people who say that they believe in God yet accept that there's no objective evidence for God. In your view, are we to call them either liars or atheists? I don't see any problem with calling them what they are - theists. There is no proof that would falsify their belief.
This is where the Russell's Teapot thing comes into it though.
If you have no proof of something's existence, then any conclusion you choose to come to can be justified by simply saying "well, there's no proof against it either". One might think that this would mean that you can just pick whatever you like. There are problems with this style of reasoning though, in that it's highly unlikely to be correct and it puts up some major obstacles to actually adapting when you're wrong.
Take God. There's somewhere between an incredibly large and an infinite number of possible gods or sets of gods that could exist. Without any other information, they're all equally likely and so there's no real way to choose between any of them.
On the other hand, you also have one more potential hypothesis, that there are zero gods. This hypothesis happens to also fit exactly with the information you have observed so far, you haven't made any observations that would support a hypothesis for a god or gods.
The other difference is that while any of the hypotheses for gods or sets of gods can be supported by observational evidence, the hypothesis for no gods cannot. The only information that you'll get that supports the no gods hypothesis is no evidence for gods at all.
This is why we start with the assumption that there's no god or gods unless there's some reason to think otherwise. This is called the null hypothesis. Because that hypothesis has as good a chance as being correct as anything else, it will be correct if nothing is observed, and is easily falsifiable by observing pretty much anything contrary to it at all.
If you were to try and falsify a hypothesis for God, it's mostly impossible. For most gods, there's no observation that can be made that would falsify their existence. These are unfalsifiable hypotheses. Even the versions of God that are logically inconsistent (like the Christian God) usually come with some caveat that He's beyond the laws of logic anyway.
Unfalsifiable hypotheses are scary, because once you accept them there's no rational way you can get yourself out, as there's nothing that you can observe that would force you to conclude that they're erroneous. This is what I meant above when I said there's obstacles to adapting when you're wrong. They're a mental trap.
Unfalsifiable hypotheses are not considered to be scientific, as science is based on observation and attempting to prove a hypothesis wrong. If something can't be wrong, then there's no sensible manner in which it can be considered to be right either.
I think a nice thought experiment that is more approachable to many people is to think about if they were the first explorers on an alien planet. They know nothing about it going in, and they're looking for life.
If they start with the assumption that there's magical rabbits on the planet, they'll never be able to disprove that even if the planet is really totally empty. The rabbits can always be over the next hill, or in another hole, or something. There's nothing that they can find that will tell them that there are no magical rabbits. And no matter how many other things they find there could always be magical rabbits too.
However, if they start with the assumption that the planet is completely dead, then either they're right or they'll eventually stumble across some sort of lifeform that will prove that their assumption was wrong in no uncertain terms. It means that at any given moment their assumption is in accordance with the best information they have to hand, and if better information turns up they can immediately throw away their incorrect hypothesis and assume the new one.
That's humans. The universe is our unknown planet, and the magical rabbits are God.
Anyway, with them it's more about not believing what they're told, or choosing to believe some invalid source of information, rather than an irrational thought process per se. To bring it more in line with the God in the room scenario, try presenting them with a local measles epidemic and see what happens.
It's very nice how optimistic you are that people will be rational when given appropriate information, and to be honest I try to think the same way when I deal with people on an individual level (at least until proven otherwise). But on a larger scale it's just not so. There are plenty of people who simply don't behave rationally. If you read through that vaccination thread there are a few good examples, and there are more on the internet.
http://www.naturalnews.com/048383_measles_outbreak_Disneyland_vaccine_inserts.html
Even after a major outbreak of measles, some people still hang onto the idea that vaccines are more damaging. Thankfully many also decide to change their minds and get their kids vaccinated.
http://www.theguardian.com/us-news/2015/jan/25/disneyland-measles-outbreak-anti-vaccination-parents
But the thing is that it's not a given that people will change their views even in the face of seemingly overwhelming evidence. To use your phrase from before, a lot of people really are that pig-headed. Actually, a lot is possibly an overstatement, but they exist and they're not exactly super rare.
If these people exist within the anti-vaxx community, I think it's fair to say that the religious and militantly anti-religious communities will probably have their fair share of them as well.
Sadly, the modern school system (and society in general, while I'm at it) tends to value memorisation and obedience over critical thinking and adaptability. And the way that society in general treats people who are wrong makes even people who realise their mistake hesitant about admitting fault and changing their mind sometimes.
It is what it is, I'm not entirely sure than my style of relentless analysis of everything is actually a positive in a lot of professions where stuff just needs to get done. For example, the operation of certain separation machines during the Manhattan Project was actually performed better by less educated operators:
The calutrons were initially operated by scientists from Berkeley to remove bugs and achieve a reasonable operating rate. They were then turned over to trained Tennessee Eastman operators who had only a high school education. Nichols compared unit production data, and pointed out to Lawrence that the young "hillbilly" girl operators were outperforming his PhDs. They agreed to a production race and Lawrence lost, a morale boost for the Tennessee Eastman workers and supervisors. The girls were "trained like soldiers not to reason why", while "the scientists could not refrain from time-consuming investigation of the cause of even minor fluctuations of the dials."
https://en.wikipedia.org/wiki/Manhattan_Project#Electromagnetic_separation
P.S. Sorry that this is such a gigantic wall of text.