Often undergraduate discrete math classes in the US have a calculus prerequisite.

Here is the description of the discrete math course from my undergrad:

A general introduction to basic mathematical terminology and the techniques of abstract mathematics in the context of discrete mathematics. Topics introduced are mathematical reasoning, Boolean connectives, deduction, mathematical induction, sets, functions and relations, algorithms, graphs, combinatorial reasoning.

What about this course suggests calculus skills would be helpful?

Is passing calculus merely a signal that a student is ready for discrete math?

Why isn't discrete math offered to freshmen — or high school students — who often lack a calculus background?

anything, including very calculus-oriented topics. Asymptotic notations, generating functions, I would want 2 solid semesters of calc in students before broaching these subjects. The distinction between discrete and calc is arbitrary to begin with, or at least does not appear in applications, hence the "Concrete Math" appellation. – Thierry Zell Sep 7 '10 at 16:57