"Then they can remove me off the plane," he replied.
"You and your whole family?" the agent asked.
"Yeah, that's fine," he said.
"So, then, it's going to be a federal offence," another agent quickly chimed in, "and you and your wife will be in jail and your kids will be -."
"We're going to be in jail and my kids are going to be what?" Schear interrupted.
"It's a federal offence if you don't abide by it," she said.
"I bought that seat," Schear said. "You're saying you're going to give that away to someone else when I paid for that seat. That's not right."
Later in the video, an agent can be heard telling Schear that according to Federal Aviation Administration regulations, his 2-year-old son could not occupy a seat during the flight and would need to sit in an adult's lap.
Schear explained that his toddler had been strapped into a car seat in his own seat on the destination flight, but the agent brushed him off.
In actuality, the FAA states that children are safer in government-approved car seats - not on laps, saying, "Your arms aren't capable of holding your child securely, especially during unexpected turbulence."
"The Federal Aviation Administration (FAA) strongly urges you to secure your child in a CRS or device for the duration of your flight," the agency states. "It's the smart and right thing to do so that everyone in your family arrives safely at your destination. The FAA is giving you the information you need to make informed decisions about your family's travel plans."
Even Delta urges parents to purchase seats for children younger than 2 and to use approved child-restraint systems during the flights.
The issue, it seems, is transferring airline tickets from one passenger to another. Delta Air Lines maintains on its website that "all tickets are nontransferable per the fare rules. Name changes are not permitted."
Eventually, Schear asked whether he could concede, move the toddler and get in the air, but an agent told him it was too late, saying his family would either have to exit the aircraft or the crew would have to deplane all of the passengers.
"So we're getting off this plane no matter what now?" Schear asked.
"I told you guys at the beginning you had two options and now it's come too far," an agent replied.
"I have two infants," he said, "and nowhere to stay. There's no more flights. What are we supposed to do - sleep in the airport?"
"At this point, you guys are on your own," she said.
Delta Air Lines said it was "sorry" for what the Schears went through.
"Our team has reached out and will be talking with them to better understand what happened and come to a resolution," the airline said in a statement Thursday morning to The Washington Post.
The incident occurred April 23 but didn't make headlines until Wednesday, when Schear posted his video on YouTube.
Fiascoes on airplanes are hardly uncommon - but they have been receiving increased attention in recent months.
United Airlines became embroiled in a public relations crisis in April when security agents were seen brutally dragging a passenger from a plane because he would not give up his seat to a crew member.
Videos showed 69-year-old David Dao being knocked against an arm rest and dragged down the aisle and back to the terminal at Chicago's O'Hare International Airport.
Days later, a passenger was booted from a Delta flight because he had to get up from his seat to make an emergency restroom run.
United came under fire again when a giant rabbit that was being transported from Britain to Chicago died after its flight.
On Tuesday, a video recorded on an All Nippon Airways flight captured a fistfight that broke out between two male passengers.
After the release of Schears' video, his wife told ABC affiliate KABC that she and her husband were justified in refusing to give up the seat. But, she said, when agents threatened her with jail time, she was terrified. "As a mother, you have a 1-year-old and a 2-year-old - it doesn't matter whether that's true or false," Brittany Schear said. "It put fear in me."
The FAA says it's a federal crime to interfere "with the duties of a crewmember."
Brian Schears told CBS Los Angeles that he and his wife never expected the situation to escalate to the point where they would get booted from the plane.
"We never thought it was going to get to the point where they were actually getting us all off the flight," he said. "As we were leaving the plane, there's four or five passengers waiting for our seat. The bottom line is, they oversold the flight."
Schear told the station that he had to eat the cost of the three airline tickets, rent a hotel for the night and then buy three more tickets the next day.