Takeo Harizaki

Takeo Harizaki - The rival character who is introduced as this one dimensional, unbeatable god at chess and this full on bully who takes great pleasure in beating players. As the series goes on, he becomes more layered and complex, and the viewer learns that Takeo was raised from birth by his abusive alcoholic father to be the "ultimate chess player," forced to play hundreds of games every day against chess simulators. It was torturous to him. While all the other kids his age were out hanging out with friends, doing clubs, sports, and school activities, he was studying the game, playing chess at every waking hour. His life was a living hell, pretty much playing chess since he could talk. He always played chess to appease his father, who only acknowledges his worth when he wins. It takes until Takeo faces off against the protagonist for his morals to change. And in the most epic character climax in all of anime history, Takeo shakes off his father's chains, and no longer plays chess for others’ approval, but — for himself…

Takeo has a special hatred for Kai because Kai's grandather was a legendary chess master who stole the grand title away from Takeo's father, causing him to raise his son to be an even better chess master (very similar to Endeavor and All Might)

We learn even LATER on that Kai's grandather caught Takeo's grandfather cheating, tarnishing his reputation and ending his careerTo make matters worse, it was the second time in the game. The first time he wrote it off as an accident, but then he realized his true intent

Except to make it less like  All Might/Endeavor, Takeo's grandfather was favored in that matchup. He was the beloved chess hero. Meaning, once convicted of cheating, he fell from a higher pedastal, making it all the more tragic