I don't get it. You iterate through the array only once. What if opposite direction pairs appear after you perform some other deletions?

Stack is a legacy class that should not be used in new code. So this is not best practice. (Deque should be used instead of Stack)
https://stackoverflow.com/questions/37314298/why-stack-extends-vector-in-jdk

sorry for the maybe stupid question, but why reverse the item when using Deque as Stack ?
from the Deque doc: "When a deque is used as a stack, elements are pushed and popped from the beginning of the deque"
why not use addFirst() and removeFirst() then ?

You could use a Deque as a LIFO queue by using addLast() and peekLast(). Then you don't have to do the reversal.

Typically this solution get best running time, but rarely it get worst than 2 for loop statement (slower than 100 * times). Try to run this 1000 times and get 1 worst case.