It's more that category theory foregrounds the functions themselves, and their relationships, rather than on the elements of sets which the functions operate on. This higher-level perspective is arguably the more appropriate level when thinking about the structure of programs.

For more detail, see Bartosz Milewski, Category Theory for Programmers:

"Composition is at the very root of category theory — it’s part of the definition of the category itself. And I will argue strongly that composition is the essence of programming. We’ve been composing things forever, long before some great engineer came up with the idea of a subroutine. Some time ago the principles of structured programming revolutionized programming because they made blocks of code composable. Then came object oriented programming, which is all about composing objects. Functional programming is not only about composing functions and algebraic data structures — it makes concurrency composable — something that’s virtually impossible with other programming paradigms."

https://bartoszmilewski.com/2014/10/28/category-theory-for-p...