It's important to remember that diagnosing someone as a narcissist should be done by a qualified mental health professional and cannot be determined solely based on one's behavior in an argument. That said, some individuals with narcissistic traits may indeed exaggerate arguments or deflect blame when confronted with their actions or behavior.
When confronted with criticism or accusations, a person with narcissistic traits might respond defensively and redirect the focus of the conversation to avoid accepting responsibility. This is often done as a way to protect their self-image, maintain a sense of superiority, or avoid feeling vulnerable or wrong.
In your case, when you confronted your child's father about living a double life and shirking responsibilities, his furious response and deflection of blame might be indicative of narcissistic tendencies. However, it's crucial not to jump to conclusions, as there could be other factors at play as well.
It's essential to recognize that communication with someone who exhibits narcissistic traits can be challenging and emotionally draining. In such situations, it might be beneficial to set boundaries, seek support from friends or family, and consider engaging with a therapist or counselor who can help navigate these complex dynamics. They can offer guidance on effective communication strategies and coping mechanisms.