(If you don't know why this is important then maybe you haven't worked on large systems that undergo rigorous evaluation)
However, it can change after insertion (if the hash bucket count changes). If the hash function is random-keyed, iteration order would be different for different instances of the hash table even if you insert the same items in the same order.
Sometimes you want the order to be consistent every time. Be it insertion order, or some natural order of the items.
A massive one - there is a lot of code that implicitly depends on the order of iteration (think configurations/initialization). The issue might be invisible, and reproduce rarely in production only. The iteration order depends on the hash of the keys, plus the capacity of the underlying array.
In Java I advise to never use the standard HashMap in favor of LinkedHashMap. In cases where data density is important both are a terrible fit having nodes instead of a plain object array (and linear probe/search).