Why people hate certain champions
This is not a defense of the champions. I am simply going to explain why people hate the champions that they do and what is okay to be considered toxic.
A champion is usually hated the most by everyone when they do lots of damage and don't die. This list of champions includes

.
But then there are the other people that are hated mostly because they do a ton of damage before you can react.
.
Some people overlap in these such as
(thank you wind wall, but I mean I'm not here to defend or attach each champion). Yasuo literally can extend his teammates CC and do extra damage with it as well as use it as a gap closer and damage amp.
The problem is when these champions have no window to fight back before they have either: a. forced you out of a fight, b. killed you, or c. don't have a true weak point.
Riven doesn't have a real weak point and also falls into both categories. I personally hate her because of this. She doesn't have a weak early game, but her late game is still pretty powerful.
The champions that are unhealthy or "toxic" are champions that give you very few windows to fight back. These champs inclue
,
,
,
,
,
,
,
,
.
The way to tell these champs are actually broken is if they have a weak point. Which
,
(although his early game still needs a few tweaks), and
do. It's their early game.
has a hard early game but it is fairly safe and has an insane power spike at 6 and lich bane which is a huge problem (6 comes really fast).
is mostly just a case of buffing a champion and adding in items that synergize with him (like the Juggernauts).
has problem very similar to Fizz but is much easier to deal with in comparison.
has the issue of he is supposed to be situational, but the way this game works gives him so much of an edge that it is more of a general strength.
is a lane bully with tons of sustain and is only really weak to mobile ranged people with high damage and can build damage and not die because his damage is also his CC (ty old kits).
THE REAL PROBLEM
I think Riot needs to look at kits and say instead of going this person is too strong lets nerf random numbers in hopes to stop them, they need to look at the true problem with each champion. Is
just too cheesy that its hard to win because you get cheesed one time due to stun locking and damage and she snowballs. Is
really in a good spot with the vast majority of damage in this game being projectiles that are on similar CDs to his wall which is instant. Is it okay for someone like
to give no fucks and walk up to your team and then kill a squishy and leave alive because their kit has a lot of chase, damage, and tank. If these are problems look at possibly removing synergy from kits because sometimes its not even a single abilities fault that the other abilities go to well together.
Look at
in S3. They purposely removed synergy from her kit instead of struggling for months to try and work out her numbers, and we finally are back to the problem of her just being so far ahead of the other ADCs because the meta shifted to her perfect position where most other ADCs fail. The meta is now Juggernauts, people who don't die and put out a ton of damage. Vayne manages to circumvent that by saying everyone dies at about the same speed and I can stay away from them to not eat the damage.