Why does it matter so much to atheists that God doesn't exist?

I do not personally care if you believe in a god or not.

I am speaking to the US Bible thumpers here, of course ~ many of whom are flat-earthers who deny evolution and see scientists as evil people who are constantly trying, and succeeding, in disproving their beliefs one by one.

Because these are not any gods rules we are talking about.

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These are man made rules - made thousands of years ago for the use of the humans who lived thousands of years ago.

Notice that I said their rules, not any gods rules.

And then use and ENJOY these fantastic scientific advancements every single day of your life?

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THE BIBLE IS THE PROBLEM!

Those rules that you are trying to reinstate are rules made by men who didn't know anything about the earth, nor anything about all of the other inhabitants of it. How can you not see that?

The people of the modern world have evolved past all of that nonsense.

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IT does not matter, mainly because it does not exist.

And how do you deny hundreds of years of advancement in all fields of science?

My problem is that people who try to shove their rules down everyone's throats - including by physical force - DO EXIST .

Is it common for Americans to feel "trapped" due to the size and distance of their country from other countries/continents? Is this feeling an exaggeration or a reality?

A belief in a god is not the problem.