Constructing a response after reading his response to critics would be good. His core reservations presented seem to be:

If you can say that there's no correct morality, why can't you say that there's no correct math, or no correct science?

If there's two different visions of well-being, isn't this just a small difference? ("This is akin to trying to get me to follow you to the summit of Everest while I want to drag you up the slopes of K2" [...] "In any case, I suspect that radically disjoint peaks are unlikely to exist for human beings.")

And he presents some rationalizations that seem to be ingrained:

"Is it unscientific to value health and seek to maximize it within the context of medicine? No. Clearly there are scientific truths to be known about health." That is, he conflates "there are truths" with "there is a truth of the sort I want."

Later he conflates 'an ideal world by my egalitarian values is possible' with 'so don't bother thinking about other peoples' values,' specifically citing selfish values. This is the logically even worse version of objection #2.