It's about play-style.
I'll be honest, Kassadin has an awesome kit. Blinking everywhere. Blinks were my favourite thing when I first came to LoL. Shunpo was my favourite ability.
Fizz is a lot of fun, and Ahri.
Irelia and Darius for me both are my favourite champions in LoL, due to being "unstoppable juggernauts", they fulfill that anime-fantasy. No matter what you do to them, they keep on going. They're the Determinators. For some reason, I can't get attached to Olaf the same way.
I used to think Xin is dull. Well, his kit is still dull, but jumping into everyone and everything is sort of fun :3
I find Vi to be awesome in theme, and very cool to play. In the end, it's about our specific thematic loves. Either story, mechanics, or just theme.
Riven's fighting game's atmosphere is also something I enjoy, and while many disagree, I get the same vibe from Vi.