Andurilas explained it better than me haha

The larger kingdom can WD on the war if you held the larger kingdom to too long of a period and unwilling to withdraw.
Note this is at least a week long war if not longer, so you need to tell your province that upfront that you want to teach the lesson to the larger kingdom from pushing you around, if you dont tell your kingdom upfront be prepared for people quitting your kingdom.

Though on the flip side, I have been in a kingdom which we were borderline almost war-able which we ended up exploring then hitting the button. The opposing kingdom were not war ready, but betting that their size will deter people and they were hitting kingdoms who could not declare war due to size difference, which lead to us winning the war. Again a long war though.....