ML is the cat painting MC drew.

She drew that painting full of emotions and treated it as a companion during her repeating days of loneliness. So ML grew up listening to MC and watching her complain, paint, eat, and suffer. MC told a lot to the painting (think of it like a man stranded on an island talking to a rock with a face painted on it), so ML knew about her repeating days and suffering. He saw her bring out the poison and finally broke free from the canvas to catch her when she fell unconscious. And that's the start.

But since our ML is adorable, he is as weak as he is cool. He pretends to be MC's doctor whose memories are reset each day to stay by her side, afraid that if MC discovers him she'll be disgusted and kick him out. So as much as he loves the attention and affection MC gives him, he hates that her emotions and actions are all for the doctor, not him.

Which is silly s*upid since MC immediately knew the stone-faced doctor had been exchanged for ML, she only calls him 'doctor' because she's afraid ML will leave when his cover is blown.

Also, they clear up the relationship situation on chapter 30, so at least we aren't chewing sweet potatoes for 100 chs.