For a particular integer consider:
“This number is either even or odd.”
A denial of the whole disjunctive judgment is:
“It is not true that precisely one of these alternatives applies under the stipulated division.”
“This number is not even” alone does not contradict the disjunction: the number could be odd, leaving the original disjunction true.
A genuine negation must address the whole disjunctive relation, whether it is an exclusive, exclusion-of-joint-truth, or exclusion-of-joint-falsehood form.