Zilean's hatred of Volibear (beyond bears in the league)
 

"I've seen your death, it was painful..."

Now I can see why Volibear hates Zilean so much, he got a vision from Zilean and it was nothing but despair, relating that to the vision he had. No wonder he hates him so much

To explain why, Volibear's rite of passage was going to receive a vision. When he got to the top. Zilean and Anivia was waiting for him. Asking for a vision, Zilean was more than happy to oblige to show Volibear the future of the Ursine and Frejord, However his visions were that of complete despair channeled into Voli.

he's a bear that hates time man. Isn't that common in your neighborhood?

Zileas was against the idea of armoured bears in this game which is why the interaction is between Zilean and Volibear.

Once upon a time there was a bear, his name was Vilbear.
So one day he joined the League and decided to hate Zilean, a time dude.
Zilean doesn't like being disliked, so he returned Vilbear the favor.
And then they went frolicking through the forest together, cause hatters gonna hat.

Zilean is obviously Stephen Colbert in disguise, yet he cannot disguise his hatred of bears

Of course, I am just stating the in universe reason beyond "bear in the league"