The Problem With Pets
So, one of the most annoying mechanics in game, in my opinion, is the Champion pet. Every champion with a pet ability (maybe to the exception of Elise and Annie) has major balance issues. This is because they rely on the minions to deal damage. Now, it's perfectly acceptable to have some reliance on a certain ability, but the nature of pets are either overpowered and painful, or weak and nonexistent. That kind of dichotomy in gameplay gimps the champion to the point where they are either way too strong, or way too weak, and Riot favors the latter over the former.
Why pets are so annoying is simple: they are abilities that absentmindedly harass the player. They take no amount of skill to use, yet they can be frustrating to play against, because you have to waste time killing the pet instead of damaging the champion. Trades are inherently unfair in this manner, because you have to focus either the pet or the champion. Either way, though, you lose. Either you get damage off on the champ, and let the pet have free reign on you, or you focus the pet, and the champion get's away with no damage taken.