From how i see it, sato was angry and slapped kei because the latter being dishonest about her supporting the former's love issue. Since kei agreed giving love advice to sato, she, indirectly, agreed to become sato's ally in this matter. Despite kei never told a lie and kept giving advice to sato, by harboring feelings and end up successfully dating kiyo, that act itself could be considered as "unfaithful"
Of course this doesn't apply if kei fell for kiyo after he rejected sato. But since kei helped sato when she herself felt the same towards the man, and end up dating him as well, it couldn't be helped that sato ended up feeling "betrayed by someone she considered ally"
This sort of thing is indeed subtle and hard to understand, even by the owner of the feeling sometimes, but this is also something that some people better express outwardly(please think twice before resorting to violence), or less would end up eating away at heart