once again thinking about this river scene because
imagine... when katsuki was shown with kindness for the very first time, he interpreted it as pity. he couldn't understand why someone would want to help him without expecting anything in return. he couldn't comprehend why and how someone labeled as 'weaker' than would want to help him when he was strong enough to get up on his own.
it makes me wonder how katsuki's upbringing was to make him question someone who genuinely just wanted to help. when he scraped his knees or bumped his head as a kid, did his parents not help him get up? why did izuku's outreached hand feel so foreign to him to the point that he mistook it as pity and looking down on him? based on the few scenes we see him interact w his mom, mitsuki probably scolded him for being clumsy and told him to get up on his own. she probably assumed he was strong enough and didn't need the help.
because of katsuki's strong quirk, everyone around him assumed he didn't need any help, and he internalized that so much as a kid that, growing up, he Refuses to ask for help even when he needed it.
before this, we see izuku still hanging around katsuki and his friends even when he was quirkless. so they were still technically friends even when izuku was quirkless. sure, katsuki called him 'deku' and teased him, but he hasn't bullied him. he still allowed izuku to join him and his friends.
i think this scene was the ultimate turning point in izuku and katsuki's friendship - it's the whole reason why he starts bullying izuku. people think katsuki bullies him for his quirklessness but that's just what he Says.
in this scene, he perceives izuku as this smug condescending guy who looks down on him and feels bad for him for falling. in this moment, katsuki starts to project his insecurities towards izuku.
when izuku reached out his hand to him, katsuki immediately realized that izuku held the true essence of a hero - someone who helps those in need - something that katsuki didn't inherently possess.
this realization turns into insecurity. they both dreamed of being pro heroes, but despite being quirkless, izuku managed to be one at the age of 5. meanwhile he has this super strong quirk but he still doesn't act like a hero, he /can't/, because he's weak.
but, instead of thinking of himself as weak, he Projects all of this to izuku, and convinces himself that it is Izuku who sees him as weak. This way, he can keep seeing himself as strong (like everyone said he was) and hate on someone else for thinking he was weak. It's a classic coping mechanism that he subconsciously did to protect himself.
unfortunately, this leads to him bullying izuku. he sees izuku as a manifestation of all his insecurities. everyone around him has always expected him to be a great pro hero. ("what if they realize i don't have that inherent selflessness that all heroes have?") when izuku applied to UA, it was a threat to him. because he knew, once people see izuku's selflessness and genuine want to help and save, they'll realize that katsuki doesn't have that same trait, and they'll think he doesn't have what it takes to be a hero. it makes him paranoid and afraid people will see he is a fraud, so he forces izuku not to enroll.
again, he projects all these thoughts to izuku, says that because of his quirklessness, he'll never be a hero. and if he wanted to be a hero, he should try to wish for a quirk in his next life. (but he's projecting. deep inside, he already Knew izuku was capable of being a hero without a quirk. he was afraid that because of his lack of selflessness, he was the one who will never be a hero. what if he was the one who was hoping that in his next life, he'd have the inherent selflessness that defined a hero?)
this makes sense with the whole Stain arc, and how he raised that the pro hero field is filled with people with strong quirks but were only in it for the money, and only a rare few were in it to genuinely help others.
and this makes the LOV kidnapping all the more tragic. The League basically confirmed all of katsuki's fears - that his traits were more fit for a villain than a hero.
but in a beautiful roundabout way, it was also Izuku - the person he projected all his insecurities to, the Reason he was insecure in the first place - who tells him he's a great hero. It was Izuku who tells him he sees Katsuki as his image of victory, that he'll be an amazing hero, not just because of his strong quirk, but because of his tenacity and strong will to win every fight against villains.
their whole thing is "win to save, save to win". because winning and saving is what defines a hero, but they only had one part of it down, they needed each other to help foster that other trait that didn't come to them just as easy.
and it mAKes sENSE now why he was thinking of This River Scene before he sacrificed himself for Izuku.
he went back to that moment all those years ago when he realized izuku was a hero. that moment when all his insecurities bubbled up.
and in his last few moments before being stabbed, he probably thought, "ah.. i wish i accepted his help, i wish i had grabbed on to his hand."