Peoples of the universe, please attend carefully.

OKAY SO "mischaracterization" might be a bit of a stretch because we really don't know much about Moriarty. But the general adaptation of him being obsessed with Sherlock's intellect, seeing them as yin and yang, seems to have been invented later. I mean, it's interesting from a narrative perspective, but not very accurate. ACD Moriarty does not care about Sherlock. Sherlock is an obstacle to his operations. The reason he cares isn't because he's deeply invested in this battle of wits, it's because he's a business man with a criminal empire and this random amateur keeps disrupting them, and I think that's important. One of the reasons Moriarty is so dangerous to Sherlock is because he has literally no investment in keeping him alive. So many times I feel like it becomes a Batman/Joker "we need each other to play this game", when that in itself would put Sherlock in a much safer position than he's in in The Final Problem. Another important piece I feel like people forget about TFP is that the confrontation at Rychenbach wasn't really a final showdown to see who would be victorious. Sherlock had already reported Moriarty to the police with a massive amount of evidence and his enterprise was about to crumble. It's purely petty, he's furious that everything he's built is about to be taken away by this guy who he met once, and he really really just wants to beat him up one on one.