Mr. Nance: Ms. Chan said that she retired from Quad Cities Corporation, and had received a watch and a wonderful party as thanks for her 40 years of loyal service.
Conclusion
At least one of them is not telling the truth.
Evidence
Ms. Chan said she retired from Quad Cities Corporation, but a colleague of hers said Ms. Chan will be gone for much of next year on business trips, working harder than ever, which clearly doesn't sound like retirement.
Evaluate
Given ... all these premise facts, How could we still argue ... neither of them is not telling the truth? (i.e. how can we argue that they both are telling the truth?)
Well do the statements contradict?
Is it possible that Ms. Chan is retiring from Quad Cities Corporation, yet she will still be gone for much of next year on business trips and is now working harder than ever?
Sure! Maybe she's retiring from Quad Cities and going into business for herself. That would involve business trips, potentially, and entrepreneurship definitely involves working harder than ever.
Mr. Nance seems to be thinking that Ms. Chan said she's retiring, as in hitting the stage of life past which she will no longer work for a living.
But Ms. Chan just said "she's retiring from Quad Cities". You can retire from a job without going into retirement.
Goal
Since this argument is using two different meanings of "retiring", we could accuse it of committing the famous (but rarely seen) Equivocation flaw.
Ms. Chan is using "retiring" to mean . Mr. Nance is hearing it to mean "entering the retirement phase of life".