It was a bold statement, even for an investor day.

"I don't think we're ever going to lose money again," American Airlines CEO Doug Parker said Thursday.

Airlines have reaped the benefits of a plunge in oil prices in mid-2014, raking in record profits. It's been a sharp turnaround for an industry that has suffered bankruptcies and recessions over the last decade.

"The old world was darkness, but now it's light," he said. "I know I sound like an evangelist talking about this."

But behind the outlook is the airline's confidence that it can wring more from passengers.

Ancillary revenues, which include items like passenger baggage fees, have been a bright spot for airlines, including American. Robert Isom, president of American Airlines, said the airline is "just scratching the surface" in ancillary revenues.

Last year, passengers shelled out a record $4.2 billion to check their bags with U.S. airlines and American Airlines brought in a quarter of that amount.

The introduction of more cabin classes, such as basic economy and premium economy, is another recipe. Isom said that since the no-frills basic economy was introduced, half of passengers are "buying up from that offering" and noted that the new class of highly restricted service is "not a price cut."

The airline is also upgrading its fleet to include thin-backed seats to fit more passengers on board, Isom said. For example, seats on some single-aisle Airbus planes will go from 181 seats to as many as 190.

Shareholders appeared to believe the CEO's sunny outlook. Shares gained 1.4 percent and are up more than 6 percent this month.

That's not to say there aren't pressures. American, the largest U.S. carrier, earlier this month lowered its revenue outlook for the third quarter following massive hurricanes.

The airline said it hasn't provided an estimate on the full cost of the storms because problems are ongoing, particularly in Puerto Rico, where operations were crippled by damage from Hurricane Maria.

Longer term, travelers who had been planning to go to the affected region may choose other destinations like Hawaii and Mexico because "we have so much of the Caribbean that's been knocked out," American's CEO told CNBC.