Writing is, as far as I can conjure, unique among creative endeavours.
A person can garden without being expected to open a table at the Farmers' Market. A person can enjoy woodworking without being expected to become a professional cabinet maker. A person can dabble in some landscape watercolours without flogging a portfolio around to the galleries. Sure, if they're exceptional in their hobbies, these people will be encouraged to share their gift with the world for fame and fortune, but it's not an axiomatic reaction.
Tell anyone that (after long arguments with your self-esteem) "I'm a writer", and the automatic response is guaranteed to include "Have you been published?"
Pick up a "How to Write" help book and 99% of them include chapters providing guidelines for submitting your work to publishers, acquiring an agent, etc, etc.
So, why can't a person enjoy writing for the sake of writing? Everyone else enjoys puttering around with their hobby in their spare time. Why does writing require swimming the icy channel to the distant shore of being a professional?
I have a thought or two on the matter, but first "Let's go to the Comments" and see what discussion there may be.