That sounds like a VERY awful story...
Then was it really cheating? I wasn't sure because it seemed so annoyingly heartless towards the MC. They live together and have sex, and it seemed like from their previous conversation after the restaurant scene, they reconciled. All of the sudden, this lady shows up and tries to get back together even though she caused all this in the first place.
I was never annoyed with either of the characters because their relationship is not as you've described it to be. I still think you didn't read the raws, or even looked at them properly. Here is just one example what you had incorrect: you mention that Chef Do kicks Yu Geon out of the house, but Chef Do *never* kicks him out of the house.
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After reading the Chinese raws, the long-haired guy is basically being given rehab by the chef MC while living in his house. He acts in ways that are outrageously infuriating and utterly embarrassing, forcing the MC to become a dining utensil, eating the food directly off his body. It seems like breaking up was too hard for Mr. Anorexia, so he also has forgone all forms of mannerism. This leads to a bad scenario where Mr. Anorexia meets his ex, and goes slightly on a rampage. This causes the chef MC to kick him out, where upon the evicted man goes to a nearby restaurant and causes havoc. The resulting police charges cause the MC and the anorexic man to realize their feelings for each other.
Several years (?)on, the couple have gotten much better. No more health issues, mostly happy with the old eating off the body thing having become more like a fetish lol. Until Mr. Anorexia meets his ex again while at work. Thus spirals another drama where the rejected man tries to single-handedly show up his ex, hurting the MC chef in the process because he thinks they are cheating on him. However, this is a ploy for Mr. Anorexia to act revenge on his ex for her fat-shaming him. The MC reconciles and they live happily ever after.
Also prepare for lots of head-banging because there were lots of parts where I was screaming injustice and telling the MC to throw out the offensive man on his ass since couldn't behave himself.