Because as the author of the article stated, learning by "teaching others" is one of the best ways to learn.
In order to teach others, people have to read the blog. Furthermore, in order to get the additional benefits from teaching others you need to interact with them. Writing a blog post that no one comments on is no more beneficial to your learning than writing a note to yourself in vim.
That is something you and the other disagree on. If you approach the subject matter as if you are trying to teach it to someone else, then your approach will be more thoughtful and more thorough than if you just want to learn it. Basically, it's a way to trick yourself into being more thoughtful in your learning.
If you have loads of self-control and dedication, by all means write yourself notes in vim and study them. For the rest of us mere mortals, it can help for learning if you are pretending to do something else (i.e. "teaching").
The primary purpose of publishing material to a wider audience should have something to do with said audience. It could be publicizing yourself. It could be a desire to help people. It could be simple narcissism. Whatever the reason, it drives the decision to publish rather than keep the material as simply a personal journal.