Why is this "absolutely wrong"? This is a natural, useful and benign description of what a function is. It doesn't contradict the formal set-theoretic definitio

Why is this "absolutely wrong"? This is a natural, useful and benign description of what a function is. It doesn't contradict the formal set-theoretic definition, which came long after mathematicians started talking about functions, and which isn't required at all to conceptually understand what a function is, just as nobody needs to know the Peano axioms to understand what the number 5 is. I don't see any harm in saying that a function is like a machine. Edit: And if really want to be pedantic, then we might as well say that a function is not a relation between sets, but just a relation (with the requirement that no element maps to two different elements), and therefore can be between proper classes as well (hence we have functors between categories). Also - there could exist other ways to axiomatize the notion of a function. They point is that the formal definition of a function is just a tool, not some metaphysical essence of what a function is.