We like to believe that we are rational beings who make rational decisions. Sometimes, we are. And sometimes, we are not.
We each have our own beliefs about how the world works and how we function in it. When we are faced with information that contradicts our beliefs, it can be almost impossible to remain open to this new information. Our brain shuts down, doing the equivalent of, "La, la, la, can't hear you," until this disquieting information goes away. In the alternative, we may listen only to the extent necessary to retrieve information from our memory to refute everything that is being said. All of this can make it quite difficult to have a constructive, productive disagreement with someone else.
The problem is two-fold:
1. Your brain loves to put things into categories. Once something is neatly categorized, once a decision has been made, your brain can relax. It no longer has to think about this topic. This topic can now be handled on autopilot.
2. Once your brain has made a decision about something, it is very invested in that being the correct decision. The time to weigh all the evidence was before the decision was made. After the decision has been made, it is, of course, the correct decision, because your brain only makes correct decisions. Your brain will actively seek out support for its decision. It will also discredit, minimize, and ignore information that would go against its decision.
So, what can you do?
1. Wait to make a decision until you have as many facts as possible. The longer you wait, the longer your brain remains open to all possibilities. Talk about the situation with a wide variety of people. Abraham Lincoln didn't surrounded himself with yes men. He actively sought advice from people who had been his staunch opponents. When you're faced with a tough decision, don't just talk to the people you know will agree with you or say what you want to hear.
2. Don't let the conversation turn ugly. It turns out that venting in anger actually hurts more than it helps. When you treat someone badly, your brain must justify why it was necessary to do so. The focus then turns to demonizing the other person so that the only logical response would be to react as your brain did. If the conversation is about to get ugly, take a break.
3. Take some time, privately, to put yourself in the other person's shoes. Think about the disagreement only from the perspective of the other person. If you were that person, why would you hold that belief? Your brain will try to tell you that it's only because the other person is a jerk or a stupid jerk or a stupid, biased jerk. You need to go deeper than that. What are the cares and concerns for the other person? What are the other person's core beliefs? How are they shaping that person's reaction?
4. We are tribal. Find a way to be a part of the other person's tribe.
You can be part of the same tribe based on gender, religious beliefs, political affiliations, family, similar interests, and so much more. Once you are part of the same tribe, you get extra bonus points just by being part of the tribe. And, you give extra bonus points to other tribe members as well.
Research has shown that Democrats will support a restrictive welfare policy if they believe it to be from the Democratic Party (even if it looks like a stereotypical Republican policy). The same is true in reverse: Republicans will support a generous welfare policy if they believe it to be from the Republican Party (and not the Democrats).
If you make this person part of your tribe, not only is the other person going to be more receptive to what you are saying, you will also be more receptive to what the other person has to say.
All of this will help you to be what your brain already knows you are -- a rational human being who makes rational, correct decisions based upon the information at hand, and who, when presented with new information, rationally evaluates it, and forms new, correct decisions based on all of the information at hand. One can hope, anyway. ;-)