Uhh, I mean, I too subscribed to Nietzschean nihilism in my teenage years, but you pretty quickly realize that it's not a huge leap to recognize that "I feel pain and don't like it, so maybe I shouldn't cause other things to feel pain as a general rule."

If we have to get caught up in objective vs. subjective, then I can just defer to the physical substrate of pain in terms of nocireceptors and the HPA axis, and then our objective methods for detecting things in others, including but not limited to: mirror neurons, blood assays, brain scans, and basic logic.