I'm thinking based on the lores we have so far, we can have different ways to interpretate the champion's personality.
Based on the current lore, Garen is an innocent "kid", he loves his family but his sister doesn't understand him, he wants a sister who understands him. He focus on trainning and fighting for his country. So the in game quotes about him and katarina can be interprated as he sees her as his comrade or sister, that way explains why there is a movie "twist of fate" where they wants to kill each other because he is jealous of her battle fame and ect.
Based on the old lore, and in some people's interpretation, Garen has romance feeling to the enemy assasin woman, katarina, it's quite dark and twisted, because katarina is a vicious and tough woman based on her lore, her in game quotes are either " never play fair" ,"Violence solves everything", or "If you run, you won't see me stab you", I do not think it's a good mate for someone like Garen, the might of demacia.
I'm not sure why people support that, though. For sure I won't like a noble warriror leader who falls in love with his competitor and especially a vicious woman like that. it's very dishonorable to battle itself too.
So which way do you prefer?