Why do computer-science majors learn calculus?
There are several answers:

Answer 1: Not all CS programs

First, not all CS programs require calculus in order to get a bachelor's degree. The Bachelor of Arts (BA) program at Mills College, where I teach, does not require calculus. Instead, we require two semesters of discrete mathematics, which we consider far more useful to computer scientists, because it (at least the way we teach it) includes:


inductive proofs
Boolean logic
proof by contradiction
sets
combinatorics
basic probability
recurrence relations
graph theory
matrices
regular expressions
finite state automata
formal languages


Answer 2: Scientific foundation

That said, getting a Bachelor of Science (BS) degree from Mills or just about any other school requires calculus as part of general scientific knowledge, along with introductory chemistry, biology, physics, etc., none of which we claim someone will necessarily be useful to a computer scientist. These courses are part of the college-wide BS core, not specified by any individual department. The idea is that anyone holding a BS degree should understand the fundamentals of major scientific fields even if they will never apply them in their careers. (Similarly, most colleges require students to take classes in history, even though they are unlikely to become time travelers.)

Answer 3: Historical reasons

Computer science as an academic discipline has not been around that long. Most CS programs started within either Mathematics or Electrical Engineering programs. Both of those fields legitimately require calculus. I went to MIT, where CS was added to the EE department. All CS majors were required to learn both digital and analog electronics, the latter of which requires calculus.

Personal thoughts

In my decades as a computer scientist, including in industry, I never used any of what I learned in the required calculus (I, II, and III), linear algebra, or differential equations. That said, they did give me the background to go into computer graphics, electrical engineering, or machine learning, had I later chosen to.

Whether programs should require calculus is another question.