Ordinarily universality might mean "applies to all members of a category." So non-UPB morality can create all sorts of subcategories of moral agents and construct arguments based on the characteristics of those categories. These moral propositions flunk the UPB tests. Why does Stef reject them? He does not really explain this in the book, but we can squeeze out the meaning.
Because Stef uses a performative contradiction as the basic move for deriving UPB, debate and the norms of debate stand at the center of UPB. Stef claims that those who engage in debate cannot deny the premises and norms on which debate relies. (Here debate is interpreted broadly, so that no one could present a disproof of UPB without engaging in debate.)
What do we know about the participants in a debate and their arguments? We know that they participate willingly, otherwise it is not debate but interrogation or something like that. They must have some common language, an ability and willingness to debate, and broad agreement on what it means to debate fairly and honestly. Without these presuppositions, debate fails as a means for seeking truth. Of course, debaters may fail to follow the rules in a particular case, either from error or from a desire to deceive, but they must put up a show of playing fair, or no one will bother to engage them.
Can we limit the time or place where a debate may occur or may have occurred? No. As long as willing participants are seeking truth, debate may proceed, between anyone, any time, any place. For that reason, the norms of debate should be similarly eternal, independent of location, and indifferent to the identity or category of participants. The only limitation that makes sense is their willingness and ability to debate.
If you have made a claim in a debate, and then go do something else, does your claim expire? Do you stop believing it and asserting it? For the most part, no, if you honestly assert something at one time and place, you could have asserted it just as honestly elsewhere, later, or earlier. If you come to doubt your claim, you can make assertions about the new evidence that raised your doubts. Hence, only a complete nihilist, who believes absolutely nothing and makes no truth claims could ever deny the norms of argument. And if he did deny them, then he would no longer be a complete nihilist. Even making an argument that X is false requires that one accept the norms of debate.
What about persons who are not yet, or no longer, or temporarily unable to debate? Appoint a guardian.
What about animals? Guardian or owner?
What about rocks? Owner.What about persons who are able to debate, but unwilling to embrace moral agency? Treat them like animals, or infants, or sages? Perhaps not sages.
Someone must take responsibility.