You've answered your own question in the response, if you're writing about how you might've made mistakes, might've misconstrued someone else's thoughts or could've handled conflict better - then you're demonstrating an ability to put yourself in the position of 'the other'.

This article isn't about writing about yourself, lots of people write about themselves. It's about writing about yourself as a vehicle with which to gain admiration and dependent validators. That ain't you my friend. :o)