The conflation between sympathy and empathy can be a big problem when you attempt to empathize with someone's feelings about a situation, but they interpret that as you having also agreed with their assessment of the situation, perhaps even including second order judgments around things like the motives and character of other participants (I felt hurt ==> the apology wasn't sincere enough ==> that person hurt me deliberately ==> that person doesn't like me ==> that person is a bad person ==> other people who like that person must be bad people).

It becomes particularly sticky if this misunderstanding persists over time, and they continue not to be self aware and eventually question why you aren't behaving in a way that is more congruent with the version of reality that they hold and believe you told them you had adopted.