Depends on how important the point is. When there is a "discussion" about an issue we need to stop, take a breath, and ask ourselves some questions about the importance of the matter and our motives.
No matter what the point is, even if it is very important, we need to maintain a high road. Honesty, self-control, a realization that the other person/people may not be able to understand the importance of getting the concepts right, an understanding that the issue may need to be revisited when they cool down, or even that they may never understand what they need to understand. No matter what, we don't want to degrade the issue by our behavior, especially if it is an important issue.
Your question makes me think of listening to the other person. Are they so rabid about their viewpoint that they could be dishonest? Are they defending themselves a little vehemently, indicating that they may feel guilty? It's good to assess what we are dealing with in a discussion before we take it too far. Lying is prevalent, but not always easy to detect so it nearly always has to be a consideration if a point needs to be made through extreme measures.