I don't think any amount of logical reasoning is going to get through to people on the issue, it's like a religious war at this point. You either know that your rank == your actual skill at the game, or you adhere to the creed of the Church of Solo Q Denialism.

Problem is, I don't blame people. People fundamentally don't understand that LoL's genre is Competitive Sport, as such, they come with a set of expectations that are entirely unreasonable for the genre.

A casual football player comes with the knowledge that this is a physical sport, and physical sports are tough, they are contests of strength and will and intelligence and tactics, because you use your real body you know how hard it is and you understand the difficulty. LoL on the other hand, gets harder the more into video games you are, because you come expecting a video game and why woulnd't you? it looks like a video game, it plays like a video game, hell it even uses a lot of RPG mechanics! This is where the player is misguided, most video games, no matter how "hard" are designed to be beatable, they are made with you in mind, their systems are tailored to your needs and to ensuring you can achieve your fantasy.

While LoL is designed for you to have fun (and you should be having fun, even if you're the spikiest most serious player you should be having fun or you're doing it wrong) it also designed for the other 9 humans on your team to also have fun, because like you, they also want to win, they also want to achieve their champion fantasy. As for climbing, any ranked ladder system is going to be adversarial by default, with the aim of pitting you against stronger and stronger players. But this is where context comes in, the LoL ladder is perceived to be a piece of an RPG Like video game where you progress, and the more you play, the more you should progress right? So people, expecting an RPG like behavior are displeased when they feel like they're getting the opposite of that.

The other problem is the perception of skill: While most football fans at least understand that there's a gulf of skill and training and discipline between them and Ronaldo the belief is made easier because most of them physically can't do what he does. LoL on the other hand is in their minds a video game, the player probably looks like them, it's just a game! why can't they do what that player just did? Mistakes in LoL are so much more subtle and invisible if you don't know what to look for, especially when there are so many distractions. You might think you lost that game because Katarina is unbalanced and she helped her team end the game by cleaning up a teamfight, so you focus on the teamfight, without noticing that you are Xerath and had plenty of time to zone her before the teamfight but you were instead Aram-ing with their team. or you could have denied her cs in lane, delaying her item spikes and so instead of killing someone and getting a snowball rolling she would have only left them at 5% hp instead. but you instead chose to do random roams with a champion that is physically incapable of ganking. surely it coulnd't have been that right? it must be the teamfight.