There are two opposing philosophical viewpoints here. Some view mathematics as a model for understanding the real world. Some see the real world as instantiation of mathematics.
Is an array a function? From one perspective, the array satisfies the abstract requirements we use to define the word "function." From the other perspective, arrays (contiguous memory) exist and are real things, and functions (programs) exist and are something else.
An array isn't a function -- indexing an array could be a function. But an array is a data structure. An array doesn't satisfy the requirements to be a function -- people are just confusing an array with array indexing.
Is an array a function? From one perspective, the array satisfies the abstract requirements we use to define the word "function." From the other perspective, arrays (contiguous memory) exist and are real things, and functions (programs) exist and are something else.