Sometimes an argument will arise between collaborators where two (or more) contrasted views or (mis)interpretations of a scientific issue exist. Sometimes both views are partially correct, sometimes they're both incorrect, and sometimes one is correct and the other is not.
Some people don't handle being wrong in a very "gracious" manner, even after realizing they are wrong, and will not admit their mistake. I have a previous experience with a more senior colleague who would not admit they were wrong even after confronted with a lot of evidence. I should also add that I was intimately familiar with the research problem at hand and they had just some very superficial knowledge of it, which probably led to their mistake. I suspect that at some point they realized they were wrong but were trying to hold the upper ground ("I'm right because I'm the more senior person") and "win" the argument. Also their ego got in the way of reason (not the first time that happened). The situation was very frustrating for me and things went sour with this person, not only because of this incident but also because of previous history.
I am facing the same problem again (with a different colleague who is also my senior) and would like to handle the situation in a less destructive manner. However, I cannot write a statement on a paper that I know to be wrong just to avoid hurting somebody's ego.
What is a good way to resolve the issue with a colleague who you know to be wrong, anticipating they may have a hard time admitting it?
Just to clarify (based on what I can read in the comments): my question is not about situations such as pointing out a mistake by the speaker at the end of a presentation, sometimes even with the malicious intention to embarrass a "competitor" (things you witness at conferences!). In such situations influencing factors are, e.g., present audience and lack of time to think things through. It's about stubbornly persisting on one's mistake even when confronted with evidence and given the time to think about it.