I would have to agree to a certain extent, people hold a natural bias simply by being human, and it's hard to rid an opinion of bias. People who complain about champions usually are those who haven't played them, or who play against them too much for their liking. The complaints against Vayne for example are mired in that she has seen a rise in popularity recently, and Vayne is very good at dueling later in the game. On the topic of duelists, most players dislike champions who are strong 1v1, since they often carry a 1v1 mentality into a team game, when the fact of the matter is that you should be carrying a team mentality into your game.
A Zed, for example, is meant to assassinate someone, they can't dive in and cc/damage heavily an enemy team, if a Zed ends up getting a pentakill by himself, I can guarantee it is because people went in on him one after another, basically sending him an assembly line of 1v1s, which he WANTS. Experienced players would laugh at a Zed trying to dive on a player when the whole team is grouped together, because the only way to successfully get a kill without giving one in turn is to be able to avoid CC and burst someone down before getting out to safety, if that happens, it a result of a) the entire team being cc'ed to allow Zed to act, or b) the Zed is skilled AND the enemy team doesn't have the ability to stop Zed before he can act.
People also have to accept that there will be champions who can naturally counter their mains. A Heimerdinger will be able to counter my main Morde in the mid lane with little effort, but against a Zed or a Syndra, who can safely poke in the former's situation, or literally move the turrets as she pleases for the latter's case, what are you going to do? Ask Riot to gut Zed and Syndra until they can't counter you anymore? If a champion has little to no counterplay, they are broken and NEED nerfing to be balanced, but if a champion beats you because he is mechanically a good counter to you, you have to accept that maybe you might not win that match. Otherwise, what would be the point of draft pick?