Cat v Dog arguement! Have I been a bad mum?

From my name you might have guessed I've got a dog & 2 cats! One cat is no problem - hakuna matata life. However, the little female one provokes the pup into fights. She actively goads him by lying close by & moving closer until she's close enough to bop him on the nose. This morning, as he made his bid for freedom through the door, she was as usual sitting in wait to lash out but this time, he head ed her as he ran by! I watched him actually think about this before the action - as if it was all a new & cunning plan! She didn't have time to respond in the normal way. Now, I don't know which one to tell off as clearly he's just retaliating & I understand that. If it were children it would be easier to sort out. Am I a bad pet mum?