it is only through empathy (identification) with an idea that you will be able to find the right counter-argument that will encourage the holder of the idea to relinquish it. (Otherwise, as I'm sure you've observed, the same argument just gets presented another way, another time.)

Related: Is That Your True Rejection?, Words as Mental Paintbrush Handles (arguments as paintbrush handles for emotional responses).

Eliezer's counter-argument in "The Pascal's Wager Fallacy Fallacy" is an example of this mistake. Arguments from the Pascal's Wager Fallacy aren't paintbrush handles for expected utility computations, they're paintbrush handles for the fear of being tricked in confusing situations and the fear of exhibiting markers of membership in a ridiculed or rejected group.