Sometimes what we say and do really matters even when the other person knows otherwise on a rational level.
In salary and other negotiations, suggesting a number will often influence the final deal. That's known as anchoring.
For example, in a simulation, people applied for jobs as administrative assistants and said that their last salary was $29,000 - which often guides the final pay offer. Some applicants joking said they wanted to earn $100,000, while others didn't. The ones who made that joke were offered an average of $35,385 - 9% higher than the average of $32,463 among those who didn't.
Even when the employer rationally knew that $100,000 was so unrealistic that the applicant must have been joking, that number implanted a feeling in the employer's head to focus on high numbers. The employer may have expected that the first set of applicants, while joking about the specific $100,000 figure, would still require higher salaries to come on board. In other words, the employer's feelings went well beyond the objective meaning of the numbers, and shaped their behavior.
When dealing with people, we need to focus on their feelings, not just the facts. In a conflict, feelings often win.