Let me try explaining the quote by showing you an example, an example that I immediately thought of when I read the quote myself for the first time:
A few weeks ago I published a post called Perfect Record. In retrospect, the prose is missing “I”—there’s no Raam in it. Now contrast that with a comment I left on the same post, where I share a story about my daily walking habit and how it inspired the thoughts about perfect records. There I am! Down there in the comments. Now the story is interesting.
Humans are wired to be sociable, to look for how they can relate to others. A human reader is no different: when they’re reading they’re looking for a way to relate to the person speaking (the writer). If the writer is not very relatable, the reader will not enjoy the writing as much as they could—they won’t be as interested. That’s why the most interesting element in any story, as William Zinsser wrote in On Writing Well, is “I”.