The inverse of the INSERT operation is the DELETE operation: given a value X and an AVL tree T, delete the node containing X and rebalance the resulting tree, if necessary. It turns out that DELETE is considerably more complex than INSERT - we will not go into the details in this course.
To illustrate the additional complexity, recall that to insert a new value into an AVL tree, we never need to do more than 2 rotations in order to restore the tree's balance. We can use rotations to restore the balance when we do a deletion, too, but in some cases we may have to do a rotation at every level of the tree (O(logN) rotations in the worst case).
Here is a tree that causes this worse case # of rotations (we're deleting X). At every node the left subtree is one shorter than the right subtree (numbers shown are height of subtrees):