How to deal with a colleague who won't accept they're wrong

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?

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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.

Answer

Hopefully this is obvious, but make sure that your language focuses on the ideas rather than the people. Rather than

I don't think you're grasping the subtleties of the situation

try

I think that there are some extra complications that need consideration in this case

Rather than taking a confrontational approach, try to adopt the role of the inquisitive student. Rather than

There is evidence in publications X and Y that directly contradicts what you are saying

try

What are your reasons for disagreeing with publications X and Y?

or

I'm having trouble understanding why the conclusions from publications X and Y do not apply here. Can you elaborate?

This will hopefully give your colleague a graceful way out without having to turn it into a matter of "you're wrong and I'm right". As a bonus, it also gives you a way out if it turns out you were wrong after all (however unlikely that is) or that you misunderstood your colleague's point. But as @R.M. and @CaptainEmacs have pointed out in the comments, take care not to overdo it, or you could come across as either clueless, or patronising.

Rather than voicing your concerns directly, put them in the mouth of a hypothetical reviewer. Rather than

I think there are these reasons for rejecting that argument

try

I think that a reviewer could object to that argument for [reasons]. I think we need to anticipate this using [different argument].