There are three hard things that come with making mistakes.
The first is realizing that you've made the mistake.
It's difficult to admit to yourself that you are flawed and are capable of hurting others (and maybe even yourself). There's a piece of everyone that wants to be perfect. And there are expectations of that as well from others. But it's important to understand that it's just going to happen. And it's best to know how to be humble and handle it with grace when you do mess up.
The second is asking forgiveness and saying you've made the mistake out loud.
It seems easier to keep quiet and hope that it blows over but closure between the parties involved is always better. Mature conversations and an open-hearted talk can begin the process of healing the relationship. Today some people care more about their pride then their relationships with others.
The third hard thing that comes with making mistakes is hopefully not experienced by everyone. It's living with the fact that the relationship may not mend.
There are just some situations that a friendship/relationship don't survive. And, unfortunately, there are some people that have a hard time forgiving and choose to not work on moving forward. This can be devastating because you feel like it could have all been avoided. Forgiving yourself and learning from what happened is crucial for your own mental health and future.
Mistakes are a part of life and they are certainly a difficult part of it. Be able to learn and to forgive and to be humble.