Here. Basically it goes like this (cutting to the chase):
(1) x IS an action or practice that will produce the worst possible misery for everyone.
So (SURELY!!!! COME ON!!!)
(2) x OUGHT not to be done.
Why, you might wonder, should we want to derive an ought from an is? We could just recognize rock bottom normative facts, like--
(3) We ought not engage in actions and practices that will produce the worst possible misery for everyone.
Harris paints himself into this corner by being so determined to extract ethics from science. He wants it to be the case that scientists come up with facts like (1) and thereby get their hands on ethical conclusions like (2). If we just started by knowing things like (3), we wouldn't know them as a matter of science. You don't find normative claims like (3) in science books.
Why's it so important to him to get ethics out of science? Because he's trying to woo the public away from the belief that ethics is derived from religion. Science is an impressive alternative source for ethics. It would be harder to convince the public that we can do away with religion as a foundation for ethics if Harris simply said we all know things like (3).
But maybe we do just know things like (3). And maybe saying so is less problematic than saying (1) entails (2). Logically, it just doesn't. Even if we do know things like (3), without relying on science, that doesn't mean science has no role to play. Armed with the knowledge of (3), we need to figure out what does and doesn't produce the worse possible misery for everyone. Science could certainly help us with that question.