All of us have had moments when our words or actions affected someone else in a way we didn't intend. It's an inevitable part of being a human interacting with other humans. It can be upsetting or demoralizing when we think we are saying something kind or helpful and the person we are speaking to takes our words as an insult. Frequently the situation leads us to have our own negative emotional reaction.
Especially when we don't understand why our words or actions had the impact they did, we might have the impulse to focus more on our intentions. But imagine you are walking past someone and you accidentally stepped on their foot, breaking their toe. While the fact that you didn't mean to hurt them might influence what they think of you as a person in general, their toe hurts just as much as it would if you had done the same thing on purpose. And, while you might feel embarrassed and upset to discover that you hurt someone, their injury is more important and should be the priority as you both figure out what to do next.
The same is true for emotional injuries. Ultimately, the person who caused the harm is responsible for their actions. Unlike the example with the broken toe, whether or not someone takes responsibility and apologizes for causing an emotional or psychological injury can make a big difference in the healing process.
Sometimes one of the hardest parts of having an interaction not go the way we intended is accepting that we are still responsible for the impact we had on someone else. Refusing to take responsibility, or focusing on our own feelings in the moment, can do further harm to that person and our relationship with them.
A key piece of taking responsibility for the impact you have on someone else is to trust that they understand their own feelings. If someone tells you that you hurt them, don't spend time and energy trying to determine if they're being honest. Just believe them.
If you are intending to be kind to someone and that is not the impact you actually have on them, don't you want to know so that you can be more effective in carrying out your intentions in the future?
For an apology to be effective, it has to keep the focus on the person who was harmed. Simply using a word like "sorry" or "apologize" doesn't automatically have the desired impact.
Here are some elements of a genuine apology:
Keep the focus on the impact rather than your intention ("I'm sorry I hurt you" sounds better than "I didn't mean to hurt you")
Don't make this about your feelings (If you appear so upset and consumed with guilt that the person you're speaking to feels like they need to make you feel better, you've created a situation where the person you harmed is actually taking care of you)
Don't use language that invalidates their feelings (Phrases like "I'm sorry you took that the wrong way" or "I'm sorry, I didn't realize you were so sensitive" make it sound like you think they are to blame for reacting the way that they did)
Avoid using the word "but" ("I'm sorry, but you did something to me too" or "I'm sorry, but I'm having a hard day" make it sound like you are trying to get credit for apologizing without claiming full responsibility)
If you talk about your own feelings and your intentions, it should be to express your intention to do better in the future ("I'm sorry. I should have realized that wasn't a helpful thing to say. I'll be more mindful in the future.")
Every mistake we make is an opportunity to learn and grow!