Cooley's partner was asked to move from his premium seat to coach.
Cooley informed the attendant they, too, were a couple but was reportedly told they could either move or get off the plane.
The couple decided to leave the flight and book their return trip with another airline.
"I cannot believe that an airline in this day and age would give a straight couple preferential treatment over a gay couple and go so far as to ask us to leave," Cooley said.
Alaska Airlines is investigating why a same-sex couple was asked to separate and move seats on Flight Number 1407 from New York to Los Angeles, though it seems the seats were double booked.
Alaska Air Group's' spokeswoman Bobbie Egan said in a statement to CNBC:
"When boarding Flight 1407 from JFK to LAX, a couple was mistakenly assigned the same seats as another couple in premium class. We reseated one of the guests from premium class in the main cabin. We are deeply sorry for the situation and are investigating the details while communicating directly with the guests involved to try and make this right. Alaska Airlines has a zero-tolerance policy for discrimination of any kind, and our employees value inclusion for our guests and each other."