"That comes totally out of the blue," said Marc Chaikin, CEO of Chaikin Analytics. "This is an extension of the fact that the consumer has not really been spending."
He noted Southwest is one of the most popular for its budget-friendly policies such as free baggage allowances.
At a conference on Tuesday, Southwest's Chief Financial Officer Tammy Romo said the airline is increasing capacity to 7 percent to 8 percent for the year, up one to two percentage points from estimates earlier this year.
The announcement caused Stifel to lower its earnings estimates on Southwest while maintaining a "buy" rating.
"We suspect Southwest is taking advantage of lower fuel prices to pursue more revenue growth opportunities—a strategy we disagree with," Stifel analyst Joesph W. DeNardi said in a note Tuesday.
American Airlines CEO Doug Parker said increases in competitors' capacity, by 5 percent to 6 percent next year, outpaces the 2 percent to 3 percent growth in demand. "That's going to have a negative impact on revenue per (available seat mile)," for those airlines, he said on "Mad Money" on Tuesday.
American, Southwest and Delta reported passenger revenue per available seat mile (PRASM) declined 2 percent or more in April from the same month last year.
The biggest inputs for the airline business are fuel costs and ticket sales, which pick up this Memorial Day weekend.
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Crude oil is up about 34 percent from its lows this year, while consumer spending has hardly budged despite the apparent savings in lower gasoline prices.
"Those two things together (recovery in oil prices and muted consumer spending) mean a little less confidence in airlines overall," said Nick Colas, chief market strategist at Convergex, a global brokerage company based in New York. "This is a one-decision trade for the airlines: How do you feel about the consumer?"
Investors have waited in vain for the spending to pick up. Retail sales were flat in April and first-quarter earnings from most retailers. The University of Michigan's consumer sentiment gauge came in at a seven-month low last Friday.
"It's hard to get overly optimistic on retail sales," said John Tomlinson, head of retail at ITG Investment Research. He noted that spending on autos and home improvement are much better than retail.
To be sure, the decline in retail sales doesn't mean consumers aren't opening their wallets at all. Increased preference for experiences over goods may boost travel spending.
"The consumer may well be spending more on airfare and hotels and experience stuff than on retailers. At some point they have to," said Michael Mussio, CFA and managing director at FBB Capital Partners, noting that lodging stocks have done well.
Lower gasoline may encourage driving more than flying, especially if fares increase.
Ticket prices could go up for Delta and United Continental, according to a Wall Street Journal report on Wednesday. The article said the airlines are taking steps to remove or limit information from TripAdvisor, Hipmunk and CheapOair.com.
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"I don't think this is a buying opportunity," Chaikin said of the airline stocks. "I think this group has had a fabulous run. I think the run is over. If the price of crude oil stabilized in this area, there's no advantage from that point of view, especially with the consumer so shaky."