If we can insert to a Fibonacci Heap in O(1), and increase-key and find-min in the same W.C time complexity, then why can't we sort an array in time complexity O(n)?
Given an array with n elements:
Find the maximum of the array (largest key) in O(n).
Build a Fibonacci Heap of the elements in O(n), emptying the array in the proccess.
Use find-min and add the result to the now empty array.
Use increase-key on the element you found in step 3, and increase it by the maximum of the old array + 1 (making it now larger than any element of the old array)
Reapet steps 3 and 4, n times. Each time a new element from the old array is added, because all added elements are larger than max+1.