Brian Schear, his wife Brittany, and their two-year-old son Grayson were on a flight from Hawaii to Los Angeles.
Before takeoff, Schear said an airline official kicked them off a flight after they refused to give up a seat they purchased for their older son.
That boy went home on an earlier flight, so the couple used the seat for their two-year-old son.
An official told Schear that it is federal policy that whoever occupies a seat on an airplane must be the person booked for the seat.
Delta said the flight was not overbooked, but there was passengers waiting to fly on standby, so they had to make room.
Schear said he was told that he could be arrested if he refused to leave.
In a statement, Delta said, "We are sorry for the unfortunate experience our customers had with delta, and we`ve reached out to them to refund their travel and provide additional compensation...."