... without making enemies:
You can sense this happening when people rush to talk over one another.
When you're in the middle of an argument, frame your disagreements in the form of questions.
This gives the other person a chance to respond without feeling cornered and threatened.
Finding any form of agreement is crucial in winning an argument, even if your position if perfectly logical. But you have to know exactly when you agree with someone (regarding which parts of their position) and when you don't.