TL;DR
Rather than trying to defend yourself, or your image, be passionately curious about the other person.
Seek to clarify exactly what the other person is saying. What exactly are the two of you disagreeing on in the first place?
There’s a chance that you’re wrong, and there’s nothing to lose if you learn something in the process.
For now, gather the facts, and come to a point where 2 + 2 = 4, whether that’s a final conclusion, or a conclusion to state that we don’t have enough information to make an accurate statement.
The biggest threat to this strategy is emotional reactivity–the need to feel good by responding quickly (the need to feel smart) and making you are justified (the need to feed your ego at expense of education). If you can delay your proclivity to respond instantly, or at least respond in questions that clarify, then that greatly reduces the risk of downfall.
A good book for reference is verbal judo.
Admitting defeat
Here’s another harsh reality: if what they say is true, then why does it hurt?
If the other side is correct in their facts, accept that those are the facts and they represent reality.
Whom am I speaking to? Who is this going to help?
The person who seems to always get in augments that lead nowhere.
My Practical Experience
How does this opinion explain how the world really works in a way that accurate, wholistic, and realistic?
Seek truth.