People who know me would say that I like to argue. I think that "argue" has such a negative connotation. I prefer either "debate" (which sounds formal) or "discuss" (which sounds informal). When having a discussion, the ultimate goal is to convince others that your beliefs are correct and that they should have the same beliefs. However, there is a much is much easier goal to achieve that is also worth the effort.
Everyone knows what are the two most controversial topics: religion and politics. I enjoying having discussions on both topics and I hope that my thoughts below will help you to enjoy them (or at least not hate and avoid them).
If you want to convince someone else of your beliefs, it is probably necessary for this person to also understand your beliefs. More specifically, this person needs to know why you believe the way you do. Based on this observation, I find it productive to understand why others have the beliefs that they do. This does not need to involve any changes in my beliefs. In return, people are likely to reciprocate and try to understand why I have my beliefs. This puts them one step closer to believing the why that I do, but obtaining this goal has another benefit as well. If you know why people have their beliefs, then you can better formulate an argument that will be convincing to them.
At this point, I would love to give an example of a discussion that I have had where the conversation not only ended with everyone retaining their original beliefs but also with everyone understanding why others had their beliefs. Unfortunately, I do not have an good example that I feel completely comfortable sharing online. If you think you have a good example, please share it in the comments.