Your writing should be useful to others. But going through the process of taking a thought and putting it down into written word also forces you to understand how you really feel about it.
By taking a situation that you have experienced, processing how it is similar or different to others depending on the context, and then breaking it down into something that will be useful for someone else, you are increasing the resolution of your own thoughts.
You are making the idea less vague and therefore easier to apply to your own life in the future.
Write for others, but even if it doesn’t reach the audience that you desire, don’t underestimate the value it brings to your own life.