When you show a linchpin strategy to a non linchpin conflict may naturally occur. The friction of your exchange of thoughts is due to a difference in beliefs. Their plan is fully tested and therefore safe and yours is innovative and therefore carries risks. One party feels threatened so the rising pressure and stress may be inevitable but what happens next can leave you a choice.
You can start a thermonuclear war with your next choice of words or find a way to turn a no into a yes.
Often the other side isn’t paying attention because he or she is busy looking at something else so timing may also be a key. In any case I suggest that you pause before you launch your first strike or to retaliate with everything you got. This is an impulse by your fight or flee response which is pretty natural and what happens us your choice.
Take it easy so you can see better options.