People can and usually do at least take something away from a political debate and or argument. A lot of time it will bring perspective, it does not mean we will suddenly see things from the other persons side of view but it allows us to further understand why we believe our way so much.
If someone has an open mind they can definitely learn a lot from a political argument. The biggest problem is that most political arguments are between liberals and conservatives and neither side is interested in what the other side is saying. Many liberals and conservatives don't have the word compromise in their vocabulary so they aren't really interested in learning they are more interested in furthering their party's goals.
Yes, you can absolutely learn from having a political argument with someone. Anytime that you have an argument, you are learning valuable debate skills that you will keep for the rest of your life. Having debates in an informal way will carry into when you have to have a professional debate.
I believe any time a person is involved in an intelligent conversation they can learn. Therefore, political arguments that present facts and truthfulness can be a learning experience as well. I think when done correctly it can get a lot of information out in the open for both sides to consider.
People cannot learn from having political arguments because they exist solely to force another person's opinion on someone else. People already know how they personally feel inside and no matter how much arguing a person does, it will not change their minds. Learning about various political groups and stances should be done in lesson form alone.