When resistance to hearing or changing meets resistance to hearing or changing there can be only one result: conflict. Sometimes that resistance sounds to our inner dialog as simply attempting to get our very correct position understood. Regardless of the motivation, the more we press our point, the more often we repeat our position, the less likely it is the other person will hear what we have to say. Resistance meets resistance does not result in resistance squared, more like resistance to the billionth degree.
Even the most aware, the most awakened of us can find ourselves doing this dance, it is not a failure, it is an opportunity to stop, take a break, listen to what we are hearing, and find another way to make our point. Maybe we can make it right away, maybe it will take a day or two, but if we keep repeating the same words at each other, common ground is unlikely, even if we both want the same thing.
It is actually the more powerful of the participants who realizes when the end of a path has been reached and another path is to be begun. Can you be that powerful?