Spoiler...
Just to be clear, the translated chapters of the novel aren't all released so it's my own interpretation from what I read.
Ian wanted revenge from the Anatold family. He dislikes the nobles (Ain holds a grudge for the Anatold and his father the ancient duke). His intentions was to kill Michel from the start however when Ian saw Michel Anatold waiting and trembling from the snow in his pretty clothes, twisted as Ian is, Ian found it more fun to play with Michel before killing him. That's why he dragged the time. He found it more amusing/satisfying to toy with Michel until the very end before discarding him.
However as you can see, one month later, Ian didn't kill Michel.
That's how we can already sense that Ian/Ain isn't a reliable narrator.
His actions/decisions don't match with what he described them to be.
Ian find meaning in the game that he started but, in which, he already lost the moment his icy eyes met those green eyes.
Why he do dat doe? Going to great lengths and shit just for him to reveal who he was. Ngl, I was expecting the secret to last longer lol. Someone spoil me pls