People formulate opinions throughout the day. They do not have the time or energy to think long and hard about any such conclusions because they must focus on more pressing issues. For most people, once they made a quick heuristic decision most will not go back and revisit their assumptions. Pushing people to rethink and use critical thinking to make more accurate assessments is likely to be met with disdain and possibly even anger making it a relatively useless strategy in most situations.
Let me say that I have some experience in contract labor negotiations and higher education so my job is/was to influence others so this is not useless advice. The key difference between those you can influence through logical discussion and those you can't is willingness.
Willingness- The willingness to learn and make new conclusions. Another term for this is open-mindedness versus close mindedness.
Those who are willing come to the table to negotiate, need advice, may want to learn, or simply are in the process of growing. They are willing to take a minute to reassess the information and how they constructed their previous conclusions.
Most people don't rethink their original assessments even when such conclusions have little logical consistency. That takes to much energy and is often emotionally uncomfortable.
To reassess a situation means that the person may be wrong, may not have been aware of all the information, or the situation has change. it requires not being afraid of adjusting ones judgement.
Healthy people like to be considered fair and thoughtful. Reassessment and judgement is a normal process while unhealthy people view it as a challenge to their self-worth. One will consider the new information and the other will argue back vigorously.
Those who should be honored are those who are willing to consider new information and make rational conclusions while those who should be discarded are judgmental and close-minded. Arguing with the latter is a useless process that is only full of frustration as no amount of "good points" will make it past their filters and will likely be met with an angry emotional response. In today's political process, it may be best not to try and win arguments but only ensure certain values and beliefs are heard!