A parent shouldn't feel badly when their child's behavior causes them to feel inadequate for it might just indicate that they're behaving in an exemplary manner as their child is comfortable expressing their true feelings!
Adults tend to believe that everyone they speak with are relating logically but this isn't true of children. Their mind is immature, they have an inadequate, often erroneous view of events and, when ornery, are simply behaving as adults sometimes do when they're ill or tired. If persistent in children this is termed Oppositional Defiant Disorder. If persistent in adults it is termed being passive-aggressive or simply being irritating.
When frequent in a child it should be investigated since it indicates their distress. Which, if not reduced, will harm their developing personality and later adult functioning. Occasional parent anxiety is normal and beneficial since it indicates their fear of making a parenting mistake and the common feeling of "mommy-guilt." But they shouldn't be overly fearful since children forgive parenting errors so long as they feel loved.