For me, what I like about Geonhu for Haeyi is that he is fun. Haeyi probably have headaches teaching this dude from the basics, but with more time spent in tutoring, surely they have some fun moments together when e.g. Geonhu successfully answers a question etc.
And well, Geonhu is actually a life saver! He literally saved Haeyi from falling down the stairs albeit in the most ridiculous way possible, using the legs. That's when I fell for him. I hope Haeyi saw that too.
Geonhu's acts of service. That's it really. The way he properly deal with Haeyi's nosebleed, the way he attacked and fight those gossip mongers because they're being too much. The way he brought Haeyi to the ice rink to skate. And in the preview for ep 14, when he cover Haeyi's feet with the blanket because they were exposed.
For what its worth, Haeyi is not bothered by Geonhu's antics. Whether or not Haeyi's unbotheredness is a good or bad thing for Geonhu's romantic pursuit to her, one thing's for sure, Haeyi is comfortable with Geonhu. And it's great to have someone like that.