A weaker argument, that is less threatening to self-worth is one way of preventing that your discussion partner goes on the defense.
Another way is to make him feel safer in the sense that he can trust that you will not hurt his feelings. This can be done by affirming that you are on the same page with him, that you and him share the same goal. You can also do this by denying what the other person might be afraid of, such as "I don't think your opinion is stupid" or "I don't want to abolish guns for hunting purposes". These methods come from "Crucial Conversations", it goes in depth on the underlying emotional motivations of conversations. Great book.
Another, cheaper tactic is to acknowledge positive characteristics of the other, making that person feel better about himself. This way, their self-worth is less vulnerable and they are more open to arguments (although this frequently fails because people distrust compliments from people that pose a threat).