It's actually a code language kind of thing for the both of them. You know, like how usual friends have their own kind of made up words for them to only understand each other. The writer personalized those dialogues into something that best suits their characters.
If you had read the mini diary entries that TVN posts, you will notice that the 'banana milk' is something very special to the both of them. The things she had mentioned during her confession were all the 'things' that held significance for the both of them, each item holding special memories which they both had shared. Thus, her confession was done in a way that gave light to the transition of being childhood friends to lovers.
As for the dialogues before their steamy scene. Her relating it to how she liked eating unhealthy junk food is more of her way of giving him reassurance and permission, rather than the 'food' mentioned itself. Since they just recently transitioned from being friends of 30 years to lovers, both of them are still awkward with each other and don't know how to act around one another. In order to overcome that, instead of being 'direct' with each other, they rather beat around the bush by using the 'code language' which only both of them could understand in order to not make things even more awkward between the both of them.
