Let's Analyze Why Lee Sin is a large source of Hate.
Be he balanced or not, I really can't say as I'm not the best at interpreting that. But I'd say these are the biggest reasons people say he is broken. He also makes some champions unviable, solely because of his existence.
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You can only dodge his Q, which is the only counterplay most people see, and his ultimate is kinda bs imho because of the mini root thing. Most people say "His only counterplay is dodging that Q" which does nuke heavillly. But warding and careful engage will save you too.
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He is in bed with Riot. He will always be meta and always be strong. Riot favours some champions heavilly, and leaves others in the dust. People hate to see other champions get all the attention and be strong, but their champion be weak and get little attention. My Swain hasn't got a skin for 4 years, so I relate.
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He doesn't fall off as much as people say. His hyper mobility, CC, reliability, waveclear, tankyness, and utility will not fall off. He can always be another tank, he can always peel the same, he can always insect, and he can always clear waves pretty easy. And even late game he can heavilly damage squishies with a Q and ult. I'm not saying he is broken, I tend to lean towards that he is not, but he doesn't fall off as much as people say imho.
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You cant counteplay him as much as he counterplays you. What I mean is that you will win most of the time because he made a mistake you capatalized on, not because you didn't mess up or made a small outplay.
AGAIN. I'm not saying he is broken, so don't downvote into infinity. I was just stating why I think people think he is broken most of the time.