The fact that your immediate response to someone trying to give you advice is to argue why hes wrong and you're right tells me a lot about what your play is probably like. You already said you're stuck in silver after two seasons. Well take it from someone who has played since Season 2, who skipped Silver IV and II last season and got placed in Gold this season. As in, i got placed into a rank that you've spent two seasons struggling to get into. I don't mean this to be rude, I just want to point out that I might have a perspective you don't and you need to stop trying to contradict everything you're given.
So let me break this down.
Well, this is League. Once you understand the fundamentals, the rest is kind of easy. With up to a max of 4 abilities, it really isn't all that complex. I come from MMOs, where you had 20-30+ abilities, and had to manage ALL of them. So, compared to that, this is child's play.
And I make a policy of never playing a champ in ranked unless I have at least 10 games on them and am confident in them -- unless it's some braindead easy champ like Kat / Yi / LB, where I do well even though I have no clue. xD
First off, the number of abilities doesn't tell you how difficult a game is. Lethal League has 3 buttons, but is that game easy? Sure, it means you can enjoy it without a burden of knowledge, but it doesn't inherently make the game easy - high level Lethal League players demonstrate an extensive mastery over the game that you cannot develop quickly. Just because a game is fundamentally simple does not mean it is easy to play at a high level, especially in PvP games.
The reason why you focus on a few champions is because you learn everything about them in all kinds of situations. You learn what their limits are, how you can most effective impact a game, how to play every single matchup to win from the start, how to coordinate ganks with different kinds of junglers, how to respond to frequent meta threats, and more. You don't learn this from watching guides or videos, you don't learn this from reading the abilities, and you don't learn this from playing 10 games. This is knowledge you develop from experience with the champion.
See, when you main fill, you can react to every situation. I pick to fill a role my team needs (not lane). If we have a lot of CC, but no damage, then I pick an assassin. If we need a tank with good catch, then I play someone like Tahm / Blitz. If we need heavy CC, maybe someone like Zac, Amumu, Gnar or what have you. Like the champion thing, I have no issue playing different roles. They're all fundamentally the same, minus support and jungle. And, after having played ~5k games since last July (when I started League), I'm pretty confident in my ability to play every role.
You can already react to situations with a diverse pool of a few champions. For example, I main top lane
If we have a lot of CC but need damage:
If we need a tank that can catch and disrupt:
If we have some AD and need AP and CC: 
If our teamcomp is well rounded: 
That's 7 champions, and includes a ranged top and an AP top. Instead of trying to pick the perfect champion out of 50, and doing mediocre on it, I can pick the most appropriate out of 7 that I'm extremely familiar with and always do well on them. Sometimes champions get added or removed to the list, but only one at a time. The advantage of maybe having the best champion for your team is not as good as being good at an appropriate champion for your team. Sure, I might have a game where in a vaccum, Gnar would be the best choice, but I play a much better Nautilus than I play Gnar, and I know how to play Nautilus in a way to fit that comp, because I have experience on the champion and know how he works from the inside out. And most importantly, when I lose a game, I know the champion so well that I can assess what I should have done in order to increase my chance of winning.
And, I know I do well, I don't just think I do. I have decent farm (usually more than my lane opponent), I have the fundamentals down, my average (over all my games on the website) KDA is 6.3:1 (meaning I don't feed, and usually do well), I usually win lane, I focus on objectives over kills, all that. The only area I think I might be a bit weak at is teamfighting, but that's only because it doesn't happen very often, and I always hesitate.
First; Here is what your stats do tell me:
The biggest thing I notice is that you have a reasonable KDA, about 7/4/8, on most champions, but you still have around 50% win rates on them, even the ones you've played the most. This tells me that you probably do well early to mid game but don't make use of your advantages, or that you're doing really well in some games and really poorly in others and lack consistency. From your match history, it doesn't seem to be the latter. So it's likely that you are mechanically fairly solid, at least enough to win lane against other Silver players, but you don't do the right things mid and late game to secure a victory. What that is varies slightly from game to game, and there's plenty of material to tell you about it. But this leads into what your stats cannot tell me:
I don't know what you specifically do that loses games where you have a lead. You might not have been doing enough damage control. You might be doing too much. You might be greeding for solo kills in the lategame. You might be farming by yourself at 35 minutes past the river. There's literally dozens of things you could be doing wrong that I would only know from watching and playing with you. Odds are there are obvious things to spot right away, but the biggest things to identify in someone's playstyle take time to observe because it's more about mentality than mechanics.
This is actually the problem that a lot of Silver players have, they don't understand that the game is more than kills and farm and turrets. I like to say that in Silver, the players know what it should look like, but not how to do it. This means, by extension, they know when they did it right, but not why it worked, and they don't know why it didn't work when it fails. Given your attitude so far, I doubt you really understand why your plays fail when they do.
Well, like I said, my opinion is obviously going to be biased. Maybe I'm horrible at everything I said, and I need to work on all of it. That's why I'm asking for someone to look at what I do, play a couple games with me, and tell me what I'm doing and what I need to work on.
Well to put it simply, if you can't escape silver in 300 games this season, you're doing something wrong. And you obviously know that, because you made this post. But you keep trying to reject everything you're told. The first thing I would suggest is to stop focusing on all the reasons you think you're doing well, because you're obviously not. 50% win rates is not an exceptional performance, it's an average performance in a slightly above average rating. Pragmatically, you're not doing anything exceptional to indicate that you are any different from the rest of the Silvers you play with. Personally, I would reckon that if I watched you play, I'd see the same kind of mistakes I see in most Silvers.
Start with the foundation that you can improve everything. Never decide that you've learned a champion. Never assume you know everything. You are constantly learning, evolving, adapting, and improving. That's how you climb, that's how you become a better player, and it's also how you do a lot of things in life.
