Who is the priority: the writer or the reader?

The most frustrating piece of advice I have been given to date is to write for myself. It's frustrating because I have always thought of my audience. Even the most personal notes I write believing my eyes won't be the only ones to read it...because advances in technology. So what's so important that a stranger should take the time to read and reflect on it? What does my experiences have to do with someone else? Some authors have the ability to turn the ordinary and personal into a universal experience or a quest to address one of philosophy's fundamental questions. But the author is writing for the audience as much as for him/herself. I think publishing the literature indicates the lesson is important or profound enough that it shouldn't be kept to oneself. So which comes first: the audience or yourself?

I suspect the professors preaching such advice mean that writing for yourself is the motivation behind the work. But if the work was truly written for yourself, why let others read it? If it's written, is the next logical step to publish? Why doesn't everyone attempt to publish? Some doubt it's any good, some works are too personal to share, financial burden, rejected by too many publishers, don't want to take the chance because you don't know what will happen, think of legacy and testaments and don't believe your work to be a necessary addition, etc. Whatever the reason, why does writing for myself need to amount to a bigger mission? Why is it not possible to write without genuinely thinking of who will read it and what will he/she get out of it?

Consider this blog. In a way, this is a publication. I wrote this entry because I'm interested to know what someone else thinks about this writer-reader paradox. I wrote it for myself. But I wrote it with the audience in mind. A stranger who is bored. Is it possible to completely isolate the two?

Lol, this is what I found on a Google search.
Similarly, what you write isn't as much about who they are as it is who you are.