One of the most difficult things about writing is catching your self on when you are censoring what is written. There are important things to write about that can be hampered by an already carefully crafted self-image.
We can be viewed in many different ways by many different people. The employee can have a very different persona to the one out with 'the lads' at the weekend. In work, censorship does exist in a big way- you must be professional at all times- you can not tell dirty jokes or express political opinions readily.
In our everyday lives therefore, we can become many different people. One of the challenges of a creative artist is to overcome such divisions. The thought..., 'What would x think of this?' can hamper the creative process and turn the work into an iodine peice of cardboard, without shape or character.
Neither is this simply a question of 'expressing oneself'- for the idea of a true self is a nonsense. There is no authentic self, just a different set of responses in different contexts.
I think it is important for the writer to de-personalize as much as possible. The work should remain distinct from the artist. Like a child, you might have been responsible for its very existence but you can not be held responsible for it after maturity.