The development of aggressive modes of response by children of aggressively punitive adults, however, may simply reflect object displacement without involving any such mechanism of defensive identification. In studies of child training antecedents of aggressively antisocial adolescents (Bandura & Walters, 1959) and of young hyperaggressive boys (Bandura, 1960), the parents were found to be nonpermissive and punitive of aggression directed toward themselves. On the other hand, they actively encouraged and reinforced their sons aggression toward persons outside the home. This pattern of differential reinforcement of aggressive behavior served to inhibit the boys' aggression toward the original instigators and fostered the displacement of aggression toward objects and situations eliciting much weaker inhibitory responses.
This entire paragraph makes me think about my own son and my childhood. I feel like in many ways I was raised in a home that actively encouraged aggressiveness to anyone but my mother. Even the smallest slights against her were met with very harsh retributions. I feel like I am that same way with my own son. Perhaps it's insecurity but I think it matches up perfectly with what Bandura was trying to say.