I don't know that book in particular, but I can give you a standard explanation that at least makes sense of the view you find puzzling.
In Aristotle's logic, any statement of the form "All S are P" implies that at least one S is P, so the statement comes out false (rather than vacuously true) if nothing is S. By contrast, in contemporary logic, "All S are P" is interpreted as saying "For anything at all, if it is S, then it is P": it is interpreted as a universal quantification applied to a conditional statement.
Crucially, the conditional statement "If it is S, then it is P" is standardly treated as a truth-functional conditional that is equivalent to the disjunction "It is not S, or it is P." Now suppose that nothing is S, so that "It is not S" is true of everything. Then the disjunction "It is not S, or it is P" will come out true no matter what we substitute for "it," because a true disjunction needs only one true disjunct. In that case, the truth-functional conditionals "If it is S, then it is not P," "If it is S, then it is not S," etc., also come out true for the same reason.
I think it's the decision to treat "If-then" statements as truth-functional conditionals that produces the counterintuitive results. But here we can perhaps distinguish the truth-conditions for an "If-then" statement from the conditions in which it would be informative or appropriate to assert the statement. A statement can be true without being, in the context, informative or appropriate to assert.