Ask yourself this: Am I trying to resolve this conflict or am I trying to prove that I'm right?
Truth without grace is just mean. It is possible to speak the truth and be gracious about how you do it.
How to escalate conflict: Insist that you know the other person's real intention even when they insist that you have it wrong.
State your opinions as opinions and not as facts. For example: "I feel cold" is a fact. "It is cold" is an opinion.