I disagree with the parent comment. It contains a thread of logic that appears to hold at first glance, but actual social dynamics are more complex and you ought to consider the full context before applying strict logic. The detailed description of the incident (Wikipedia link from GP) suggests that the airline mishandled the situation from the start:

> Several passengers stated that the situation escalated quickly and was inflamed by the demeanor of a United employee. According to passenger Tyler Bridges, "An airline supervisor walked onto the plane and brusquely announced, 'We have United employees that need to fly to Louisville tonight. ... This flight's not leaving until four people get off.' That rubbed some people the wrong way." Passenger John Fuller described the employee's behavior and said, "She was very terse. ... She said, 'Four people need to get off this plane, or we're not going anywhere.'” Passenger Jason Powell corroborated this account and said that he did not understand why the employee had spoken with such a belligerent tone: "The tone immediately turned me off ... She accelerated the situation. It was poor leadership."

No one on the plane accepted the initial offer of $400 in travel vouchers to take the next available flight, nor the follow-up offer of $800 in travel vouchers.