In a video uploaded to YouTube, Schear told a flight attendant, "I got him a ticket on another seat and you're saying you're going to give that seat away to someone else?"
Schear said the airline told him that because his oldest son wasn't using the ticket, they needed to give the open seat to another passenger.
The Schears bought that seat for their oldest child, but the only way they could have used it would be to cancel the ticket and re-purchase it in the name of their younger son, incurring cancelation fees and paying extra for the last-minute fare in the process.
Schear said he had originally booked the seat for his older son, who had taken an earlier flight to make sure one of his other children would have a seat.
Later in the video, another employee said that Federal Aviation Administration rules stipulate that a 2-year-old can not be in a seat, or occupy a auto seat, and needed to be sitting an adult's lap.
When he responded that there was nowhere for his family, including two infants, to go and no more flights, the crew member can be heard saying: "You guys are on your own".
Even Delta urges parents to purchase seats for children younger than 2 and to use approved child-restraint systems during the flights.
Schear told NBC 4 that he informed airline staff about the situation before the family boarded the plane.
On the video, a person on camera - whose identity is not clear - tells Mr Schear: "You and your wife will be in jail.it's a federal offence if you don't abide". When Schear's eldest son booked a seat at the last minute on an earlier flight, Schear made a decision to use the original seat for his 2-year-old instead.
"Trying to help us would've been not overselling the flight and not trying to force us to get him out of that seat that I paid for and holding this whole plane up", Mr Schear answered. They put their 2-year-old child in a seat they paid for.
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However, the Federal Aviation Administration "strongly urges" infants be in vehicle seats and permits adults to hold children under 2 in their laps.
Brian and Brittany Schear were flying from Maui to Los Angeles with their three children, reportedly ages 18, 2 and 1.
Delta announced that it was sorry for an unfortunate experience and would be compensating the family. Join the discussion on our Facebook page.
Following the United incident, Southwest Airlines Co LUV.N said it would stop overbooking its flights. "That did not happen in this case and we apologise", said the airline.
Brian Schear and his family were aboard a flight headed to Los Angeles.
Delta Air Lines has offered an apology after forcing a family off an overbooked flight in April.
The Associated Press reports that the Federal Aviation Administration "strongly urges" that infants fly in a auto seat, however, it allows a parent to hold a child under two in a lap.