I love this quote from poet Rainer Maria Rilke: "A person isn't who they are during the last conversation you had with them—they're who they've been throughout your whole relationship."
Do you sometimes obsess over a recent conversation, whether it's one with your partner, friend or perhaps your child? You chew the words over and over, growing more upset with each chewing! Yes, I've done that more than I care to admit, too.
It's always good to keep Rilke's words in mind, though. The words and conversation need to be held in context with the whole of your relationship with that person. If those words really are symptomatic of the relationship, then perhaps it's time for you to decide what to do about that. Is this relationship one that's healthy for you? One you want to keep? Does it need some major work or minor tweaking?
If, however, the conversation seems to be a fluke (perhaps the other person was having a bad day or misspoke—or you might even have misunderstood), consider it in the full context of your relationship. When the words were hurtful—even if on the whole, your relationship is good—they still need to be discussed with the other. But the conversation might look entirely different when you think about other things that person says or does.
It's so easy to react rather than respond to words we don't like. Take your time. Consider your response based on your relationship and history. Then proceed carefully and thoughtfully.