The definition of insubordinate is someone who is not submissive to authority or that is not following orders.
When you talk back to your boss and refuse to do what he has asked you to, this is an example of when you are insubordinate.
not submitting to authority; intractable, insolent, disobedient, etc.
Origin of insubordinatein- + subordinate
an insubordinate person
Not submissive to authority: has a history of insubordinate behavior.