Ever lose an argument where you were right?

Last week at work, a coworker started an argument with me regarding how we are dispatched to jobs.
Admittedly, I was not feeling well (i have had a cold), and I wasn’t prepared to defend my position. He deflected the issue, and blamed me for not following the rules as he saw them. I was flustered and self defensive, and I have no doubt I lost that argument.
The problem is I was right.
I am going to try to discuss this again tomorrow morning, to make sure my point is made.
Have you ever lost an argument where you were right? How did you resolve it? Did anyone notice?
I equate this to an innocent man being found guilty due to bad lawyering.