So far, Damon's concept of Liebe is always been that of 'a quest' where he had to work in order to win against an opponent.

He fell in Liebe with Katherine when he already knew that Stefan had serious feelings for her, even if he was reluctant to act on them. We can assume he started flirting with her and competing with Stefan as a game, and it later turned in something Mehr intense because Katherine was so different from any other woman he had met and he felt stifled Von the life he had.

Katherine was his escape from a life he did not want, and most especially from the life his father wanted for...