Why do you think students have difficulty understanding the concept of a mathematical function?

Because they have never had to express one quantity in terms of another. The idea of such a relationship is completely new, as is the vocabulary for expressing such relationships.

Step-by-step explanation:

"Function" is a simple concept that says you can relate two quantities, and you can express that relationship in a number of ways. (ordered pairs, table, graph)

The closest experience most students have with functions is purchasing things at a restaurant or store, where the amount paid is a function of the various quantities ordered and the tax. Most students have never added or checked a bill by hand, so the final price is "magic", determined solely by the electronic cash register. The relationship between item prices and final price is completely lost. Hence the one really great opportunity to consider functions is lost.

Students rarely play board games or counting games (Monopoly, jump rope, jacks, hide&seek) that would give familiarity with number relationships. They likely have little or no experience with the business of running a lemonade stand or making and selling items. Without these experiences, they are at a significant disadvantage when it comes to applying math to their world.