Often, they are never meant to hurt - acts done with little conscious awareness of their meanings and effects.The statement isn't just applicable to microagressions, or even to negative interactions. In fact, I think there is often an imbalance in how significant an interaction is to the different parties involved.
In fiction, there is a tendency to ascribe a single level of significance to an event. After all, we know as the author if something is important. Readers are also quite trope savvy from a lifetime of storytelling culture, and are good at spotting plot-relevant details.
The characters, however, don't have these meta insights. They ascribe meaning to words and actions based on context, including their relationship with the other character, their life experiences, and their feelings at the moment. What might be a throwaway comment to one character might be interpreted by another as genuinely inspiring words or encouragement, or confirmation of a simmering suspicion, or a stinging verbal cut.
This difference in interpretations is a credible source of miscommunications and conflict between characters without having to resort to a contrived 'big misunderstanding' plot. Even if the plot doesn't hinge on it, these moments can be crucial pieces of character development, and even give some insight into the social dynamics of your world.