It remains unclear if beginning a conversation with 'Good day' as a greeting is right or wrong and most persons argue that it is right as the term could serve as a substitute for any fraction of the day.
I think 'good day' is more than just a greeting but a wish as well, how?
If you just ended or about to end a conversation with someone at a time where the sun is fully dead from your cardinal point, won't you end it as; 'Good night?'
Would you begin a conversation with 'Good night' as a greeting to someone you just met in a dark hour?
Ultimately, beginning a conversation with 'Good day' is wrong and must be avoided especially when one finds himself in a formal setting such as meeting with your school lecturer, your strict boss and persons of these calibre.

Paulinus Sunday
(Open to conflicting opinions)