That's true, in the theoretical sense. Algorithms can be described in English or in mathematical notation. Runtime complexity of an algorithm can be calculated by hand. Most often, we want a way to also evaluate those algorithms, to take measurements on their behavior, and to understand them more intuitively. Computers are useful for that, but only if there's have a way to give them instructions. It follows that a student must be taught the rudiments of programming to have an automated method to explore the properties of algorithms.
This is analogous to the use of scientific instruments in astronomy. Everything can be done by hand (technically), but tools make things quicker and easier. They act as force multipliers to make more things practical to do in a shorter amount of time. For astronomy, that means that the astronomer doesn't need to be a million times closer to the thing they're observing in order to see it clearly. For computer science, it means that I don't need to evaluate a billion algorithmic steps by hand.