It is the logical extension of noticing the similarities between yourself and others, and noticing that you do not enjoy pain. It’s certainly not mathematically rigorous, but it follows from simple reasoning nonetheless. If you wanted to be rigorous, you can’t even claim that you don’t like pain, only that you haven’t liked specific instances of pain in the past. Some estimations are necessary for a functioning framework of any kind, including ethics.
I agree that it’s possible to arrive at the conclusion “pain is bad” as an individual, but I guess what I’m arguing is that there’s no absolute hard line on what is and isn’t ethical. Each individual person might have their own personal line, but there is no guarantee that line will be the same as another person’s. Case-in-point, a psychopath is someone with reduced or no empathy for others. They may very well not consider pain in others bad at all.
So? Just because someone chooses not to follow the reason, that doesn’t make the reason invalid. If anything you’re only proving the failures of a passion-driven ethical model, if the psychopath’s passion is inflicting pain there’s nothing to keep them from behaving unethically.