"Why not a proof/Sign/indication" - challenge and various responses to it in Quran.

[SaStrike]

I can agree with your analysis to this point.
Continue; please.

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Why not a proof/Sign/indication

Sura 14, The Quran:
( 9 )   Has there not reached you the news of those before you - the people of Noah and 'Aad and Thamud and those after them? No one knows them but Allah. Their messengers brought them clear proofs, but they returned their hands to their mouths and said, "Indeed, we disbelieve in that with which you have been sent, and indeed we are, about that to which you invite us, in disquieting doubt."

( 10 )   Their messengers said, "Can there be doubt about Allah, Creator of the heavens and earth? He invites you that He may forgive you of your sins, and He delays your death for a specified term." They said, "You are not but men like us who wish to avert us from what our fathers were worshipping. So bring us a clear authority."

Sura 6, The Quran:
( 111 )   And even if We had sent down to them the angels [with the message] and the dead spoke to them [of it] and We gathered together every [created] thing in front of them, they would not believe unless Allah should will. But most of them, [of that], are ignorant.

( 112 )   And thus We have made for every prophet an enemy - devils from mankind and jinn, inspiring to one another decorative speech in delusion. But if your Lord had willed, they would not have done it, so leave them and that which they invent.

Yes MK; You are correct; these verses also prove that even if the clear signs were shown; if God didn't will for the soul to believe; the person won't believe.
You are correct in your analysis.

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But implied is that,  some people demanding proofs will not accept proofs. And this the other side of the issue which Quran will elaborate on.

THIS. Exactly.
This is a good topic. Continue.

Doesn't prove anything. In fact it just makes it more ridiculous. For example, if I make up a religion on the spot, and write in my book: "People won't believe this" then when they end up not believing I can't claim I predicted the future or I'm right etc. Please...