Why do you think they are mutually exclusive? Generating functions, geometric series, difference equations, integrals over discrete probability distributions, elliptic curve cryptography, general linear programming and optimization, eigenvalue analysis in graph theory, stochastic optimization, all these things involve calculus to solve discrete algorithmic questions.

In fact I’d argue it makes calculus more important than what is typically understood as “discrete math” because in order to have the mathematical maturity to really understand the meaning of major discrete math results and theorems, it requires understanding calculus first.

If you “just” study discrete math mistakenly believing “that’s where the value is” then you’d end up with a shallow understanding of discrete math, lacking ability to extract value from it except in some narrow sense from rote discrete math application-specific coursework.