The senior tight end was among several players who voiced their objections to school president Ray Watts during a meeting in which he told the team's players, coaches and staff of the decision.
"My son asked me last night, 'Hey Daddy, what are they going to do to the program?'" said Henderson, who spoke from the front row just feet from Watts.
Henderson, 26, a former MP in the Army who did a tour of duty in Iraq, left little on the table in his response to Watts, raising his voice to a fever pitch and at one point standing up and stepping closer to Watts.
The moment was captured on video from several rows back, closer to the rear of the room, and posted to YouTube.
"He looked me dead in my eye and asked me, 'What are they going to do?' My 3-year-old ... what am I supposed to explain to him?" Henderson said.
The university then announced the decision as several hundred UAB students and fans gathered outside for the third straight day in efforts to support the program.
UAB made the decision after a campus-wide study conducted by a consulting firm over the past year.
"You're telling me it's because the numbers didn't look right? The numbers didn't look right?" an emotional Henderson said. "And you'll go home and sleep in a comfortable, big-ass house. But it's OK."
Henderson said he was turning 27 in a week but there were 17-year-olds and 18-year-olds on the team, too.
"What are they supposed to do? Some of these cats came from 3,000 miles away and came right here to be a part of this. To be a part of all of this," Henderson said. "But you say 'numbers'?"
In the video, an older man then approached the front of the room, presumably coach Bill Clark.
"This man walks to you, walked in your office and said, 'You've got to do it the right way for me to be here,'" Henderson said, pointing at Clark. "And you said you would. And now you just pull the plug? So you lied to the man's face?"
UAB said in a release that it subsidizes $20 million of the athletic department's operating budget of some $30 million annually and said both those numbers rank fifth in Conference USA. The university said the difference over the next five years would be an extra $49 million with football, including a projected $22 million needed for football facilities and upgrades.
Players met later Tuesday and agreed they would like to play in a bowl game if the team is selected for one, a source told ESPN's Joe Schad. The Blazers became bowl-eligible after Saturday's 45-24 win over Southern Miss, finishing 6-6.
UAB is the first major college football program since Pacific in 1995 to shut down.
Information from The Associated Press is included in this report.