Let's continue this hypothetical for a minute. So a player asks you, as a DM, to play an evil character. You respond as above: that they can't since your abilities as a DM simply don't extend to making an enjoyable campaign for an evil character. The player then responds: "But you're such a great DM! I have the utmost faith in your abilities! I've been thinking about this character for weeks... I've got all the details worked out, this incredible back story. I've put so much effort into this... I'm positive that you can make this work."
What happens now?
Anyone who actually knows me well enough to be
able to say such things would not actually do so (as they would be knowingly speaking falsely), so the question is moot. I understand what you are going for--you want to produce an irreconcilable conflict. The whole point of the thread, it seems, is that a lot of people think nearly every such question is irreconcilable and thus you absolutely have to have someone make a display of power to permanently silence discussion. I reject this notion, both because it relies on zero-sum thinking, and because it simply ignores that, in practice,
extremely few such things are actually so pointed.
If the player is willing to discuss it with me and we can find something--
anything--that falls short of, as I said, "unrepentant evil," then perhaps I can provide them what they seek. They will almost certainly need to make sacrifices, probably quite a few sacrifices, to their as you put it "incredible back story." I certainly am prepared to make such sacrifices when I bring concepts to a table.
It would be honestly quite flattering to be told I am a great DM (something I still struggle with believing.) And to know that they have invested a lot of work into it is great, I love supporting genuine and sincere enthusiasm. But the fact of the matter is, I
cannot provide enjoyable gameplay for truly, unrepentantly evil characters in anything like a "campaign." I can't even
roleplay one as my own character (every time I've tried, I've failed. And I really did try on the second go round, even going as far as cannibalism! The IRL guilt caught up with me.)
If we can do
literally anything short of "unrepentant evil," I can probably make it work. Like I said, former evil, tempted good, bastard neutral, person plagued with insanity or possessed by some other force...there's all sorts of stuff we can do that includes dark themes and connections to evil. I find it fairly unlikely that anyone who has such a positive opinion of me would be
truly so unwilling to consider anything but the absolute, line-by-line perfect retention of what they brought to the table. (Which, to reiterate yet again,
that's not what compromise is.) If they can't meet me in the middle, then I
definitely can't run a game for them, not because of any preference issue but because they're being just as demanding and problematic as the DM who says, "I won't let you do X because I think it's stupid, we will not discuss this further or you're out."
Your intended example has already crossed that line: they refuse to discuss, they demand only fulfillment of their original story (constructed in isolation, without consulting me or, presumably, anyone else) and will accept nothing less. There is no difference between this and the DM who simply rejects a player request to play tiefling or dragonborn or whatever without discussion, demanding only fulfillment of the terms they unilaterally declared and accepting nothing less.