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However if the demon does make a prediction and your action is opposite of that prediction, then determinism has failed. Free will exist.

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So by that reasoning, my computer program would have free will too. You KNOW the inner workings of the program. And you can predict with certainty what it will do. But you have no way of entering that prediction into the program and have it come true. I've just created a computer program that has free will. I'm a genius, no?

Paradoxes (however absurd) do not mean free will exists.

Yours is somewhat like saying time travel is impossible because of the grandfather paradox. But, it's not even as impressive as that, really. The demon could still predict your action (but not tell you), and you could still go back in time (but not kill your grandfather).

At this point, you either realize you were wrong, and your stubbornness is causing you to continue this line of reasoning; or you don't realize it, and you... well... nevermind.