Every person who doesn't empathize with others is a narcissist?

One of the possibilities is that they are a self-centered self-obsessed narcissist who doesn't care about anyone around them. Another possibility is that they themselves are in a traumatized state. They've been through something so terrible that they've grown emotionally numb and are desperate to feel something. In that process, they unknowingly end up harming others and regret it later.