The negation of "every student passed" is "no student passed".

False

False. $\lnot\forall x\,P(x)$ is $\exists x\,\lnot P(x)$, some student did not pass. 'No student passed' is $\forall x\,\lnot P(x)$, a far stronger claim. Confusing the contrary with the contradictory is one of the most common quantifier errors, and it is why a single counterexample settles a universal.