Round trip required?

Coming down Saturday On a 1 way ticket. Didn't make a return reservation due to an Easter "glitch", so return is a little bit up in the air. But planning mid to late April. A friend advised me that a round trip ticket is required before an airline will allow you to travel. Correct or not?

A boarding agent wouldn't let us on a Delta flight in Atlanta without a return. We showed our Residente Permanente cards and it worked.