For people who say this is abusive relationship because of that dog thing maybe didn't read beyond that. Kyoya treat her like a dog BEFORE they date. If I try to defend Kyoya, then I will say he loves dog. And he clearly doesn't know how to treat other people.
What's the most important is, will Kyouya change? YES, a lot. That's character development. Kyoya NEVER affect her pyshical and psychological condition negatively, vice versa when they date each other. That's what usually happen in abusive relationship but I never see it happen here. They are flawed but they know each other really well that they can see each other through their flaw that many people fail to see. He is also surrounded with friend who understand him. Other than relationship with Erika, I also like to see his friendship with the others.
The thing is, Kyoya has difficulity to show affection to someone else most likely because most of the time he is alone. I think his sister who often slap and bully him also have influence to develop his character like that. Even if he has friend, his friend never show affection like how someone do to their family or loved one, so he often show how he is confused what to do to Erika. Then he usually observe and take advice from his friend. From this he learn and become gentler and initiate many things to make her happy even if he doesn't like it. Erika is also develop from someone who often push her idealism to Kyoya (Ex: She want to flirt in public, but it makes Kyoya uncomfortable) but she change to be more considerate. Both of them compromise really well. They never push their partner limit and their power also balance. Kyoya speak harsh even now, he doesn't like sweet talking so he is harsh when he said his opinion but everytime Erika doesn't agree what Kyoya said, she will speak up and he will compromise. One example,
Erika want to help Takeru's cafe because it's about bankrupt but Kyoya didn't like Erika wear maid uniform because many people seduce her. Erika didn't want to listen and still want to help because she is concerned with Takeru, so he compromise by become butler instead so his girlfriend didn't have to wear maid costume though he is tired to smile all the time and hate sweet talking.
Even if both of them change, we can see deep inside they are the same person. Both of them show it especially when they are angry or anxious, there is one time when Kyoya ever said Erika is a bitch and also one time when he bring her to his house he was kissed by someone else. But later on they will realize they are wrong when they calm down. Well, human is like that. Even if we change to be better person, our core personality is the same, we can only lower our bad side, it can't completely disappear.
What's so unhealthy about that? I am wondering why people think this is unhealthy. But I agree maybe some people can't really see their relationship as healthy because they start that way but that's what we call character development. For me, to see a character with personality as bad as Kyoya to slowly change through their relationship is really enjoyable. I actually read this when I was in middle school long ago and it helps me learn how to compromise.