TLDR, I quit because the game wants to go faster and faster and that shoves more and more options out of the gameplay pool and forces content creep.
Pedantic aside I started in S3 and quit in S7 because games became spikefests-- the first champ to hit power peak usually carries their team with them to victory.
The snowbally direction of the game spoke about its future, and I knew for sure I wasn't going to keep enjoying a game where fights weren't planned as much as three people pressed R at the right time. I think a lot of people can list three man wombos that turn games and teams inside out.
I think I ultimately left because it seemed and even now seems like Riot, League's creators, are even proud of this direction the game is going. In the end, I think what I wanted out of them was to make teamfights a thought process. But they were assuredly not making them so, and even after I've all but uninstalled, they've gone and released Zoe. The game is not headed for a healthy direction in this guy's opinion.
But I'd suggest you play it, see how you like it after they release a new champ, or rework someone. Get a feel for their balance direction. It's one of the many many MOBAs, and it's free. A month or two to give it a solid trial shouldn't be too much.
What do you want out of a MOBA? For me, it's teamfights and HotS is teamfight-centric. DotA has an intense lane-phase, and SMITE is a hit with everyone I know who doesn't like any other MOBA on the market. That's about the extent of my knowledge on the genre but I'd say LoL holds a place with the most sheer content thanks to 139? individual champs.