A reason for a diary to be kept private is that it contains one’s thoughts in one’s own language. Which is different from expressing an idea to someone using terms that they will understand. A diary is mainly to write back to one’s self, so that he can remember what he was thinking, or of what the context of his life was at a certain time.
But even if you aren’t intending to keep a secret from someone else, it won’t always be in a form they would understand or construe correctly. There’s none of the background information, or elucidation; which might be more confusing than not in the hands of someone other than its author. And why always write so that others can understand? That’s exactly what a diary is for: Somewhere to transcribe your thoughts themselves, and not their outward form.