Another element that factored into their decision included United's "Clear Record of Sustained and Substantial Underperformance."
"Despite premier, industry-leading strategic assets — such as significant scale advantages, strong brand recognition, hubs in key business markets, and membership in the largest global airline alliance — United has been the worst performing U.S. airline stock over the last five years," Altimeter and PAR said.
Over the past five years, United shares have gained nearly 128 percent, while the S&P has risen 52 percent. But shares of rival Delta have risen more than 300 percent during the period and Southwest Airlines' has gone up 224 percent.
Bob Crandall, former president and chairman of American Airlines, said Tuesday that expectations for airlines have risen substantially. "The consequence of that is activists saying let's see if we can get some pros in there, and maybe they can help United do a little better," he told "Squawk Box."
"I think the activity itself is probably a consequence of United … being in an unsteady situation for a long time," he said. "They've never gotten that quite right since the merger."
However, Bethune agrees with Altimeter and PAR's read on United's potential.
"They should be in first place instead of fourth or fifth place. United has the best employees, the best fleet and the best route system," he said. "If you're in a horse race and you're in fourth place, you're not winning."
— CNBC's David Faber and Phil LeBeau contributed to this report.