How can one reconcile the prohibition of publicizing sins with avoiding hypocrisy when committing them or persisting in them?

Committing a sin is ugly, and what is uglier is to openly declare it. It is obligatory upon a Muslim to abandon sin in private and in public. Not every act of disobedience is called hypocrisy. Hypocrisy is of two types: major hypocrisy, which expels one from the faith, and minor hypocrisy, which does not expel one from the faith but coexists with the foundation of faith.