1) Dragon RNG - To be fair, drake rng doesn't decide games too often as it is right now. Next season however, Riot is making it so that drake rng will heavily benefit one team over another. So now I might get in my series, and lose a game because the air drake spawned 3rd, benefiting the enemy Hecarim. If that happens, because of sheer bad luck, I will be in a situation where I have to protect the air drake from getting taken, just so I don't buff Hecarim; I will not be able to take it for myself, because I'd only be helping the enemy team. This means I can't play for Elder drake. It's dumb because when you increase the influence of randomness, you diminish the influence of skill.
2) Invisible Assassins - This is an inherently broken champion concept. Why is it that Evelyn can 1 shot me out of thin air? There is no counter play to this whatsoever. If you can get into a position to kill me before I can react, it is broken. This is anathema to skill because there is no way to use my skill to outplay it.
3) Carry Supports - This is an inherently broken champion concept, because it breaks the competitive nature of the game. Due to high base damage, and typically true damage or %hp damage, these supports can out damage the true carries on their team without taking any resources. Everyone but them has to compete for resources. This is anti-skill because you can fulfill the damage dealer role without having to go through the skill intensive motions of competing for cs or kills. Even if you feed on Brand you still do high base damage and 16% + 4% of my hp in magic damage.
4) League is Pay to Win - This is simple. The hentai bait League of Legends champions are very popular, and so they sell a lot of skins. In return, Riot buffs these champions to make them extremely broken, so that they sell even more skins. Examples include Ahri (she is constantly between a 52-55% w.r with a high lay rate), Riven, Kai'sa, etc... I mean when are Ahri, Riven and Kai'sa not good? They are always staples in their roles. Now people might say "Oh Riven's win rate is 50%". First of all, she has a high skill cap, so if a champion takes a while to learn they should have a lower win rate. Second of all she has a high play rate, meaning there are a lot of people playing her who don't know how to play her well. Third of all, she has a high ban rate, meaning when she does get played she is getting played into counter match ups more often. Fourth, there is a selection bias for some of these champions (like Riven), in that you're more likely to pick Riven if you've never met a 1v5 you don't like, or are toxic, or have weak impulsive restraints; all of these things make you more likely to lose. This is anti-skill because if your champion is busted on the grounds that it sells a ton of skins, it will inflate your effectiveness in game without you needing to be as good as your opponents.
5) Giant handicaps - Okay there is 1k shutdown gold in the game now, which scales up very quickly. It has gotten to the point where if you die to your lane opponent from a gank, you basically lose like 1/2- 2/3rd of your gold lead. Also there is shutdown xp which no one even talks about. So kill xp is calculated by taking half of the xp your opponent needs to lvl up, and then adding 7% for each lvl you're behind. Have you ever killed someone you're two levels behind? You literally just level up off it. In conjunction with the fact that you deny them a minion wave or two in the lane phase, while picking up minions of your own, you basically just remove the experience difference if you get a single kill on someone who completely out-skilled you. Handicaps are inimical to a skill based game because... THEY'RE HANDICAPS. OH MY GOODNESS. WHY ARE THERE SO MANY HANDICAPS!?
6) Jungle Incentives - Junglers are incentivized to just sit on their lanes all day. If you're ahead of the jungle camps in level, you lose x% of xp off of them (depends how many levels you're ahead of them). This means if you have a level lead, you don't want to farm to grow it more that way, you want to use your lead to gank instead; farming with an xp disadvantage would be inefficient. If you're even in level you also want to gank, because you can just get catch up xp if you are behind the jungle camps in level. If you're behind in level, well then you just farm a few camps and you're back to even (anti-skill handicap by the way). After you are back to even you of course return to spam ganking your lanes. This is anti-skill because the lane phase is supposed to be an opportunity for you to build an individual lead over your opponent, but instead it is just a contest of "well who's jungler ganked more?"