Somebody called it "a debut," which wasn't true, of course, because Argentina has had a mission in Washington for 170 years. Still, after being held at arm's length by the Carter administration for nearly four years over Argentina's human rights record, there was something of a coming-out party about it.

Suddenly, it seemed, back in favor Monday night was the elegant Q Street dinner table of Ambassador and Mrs. Jorge A. Aja Espil where 38 black-tie guests assembled to honor Chase Manhattan Bank President William Butcher and his wife Carol.

If none officially represented the policy-making levels of the new administration, the upbeat mood of pro-Reagan bankers and businessmen suggested it was only a matter of time. (At the State Department, for instance, the assistant secretary of Latin American affairs hasn't been named yet.)

So Ambassador Espil talked optimistically of Argentina's economic prospects and businessmen talked optimistically of their trade prospects in Argentina. Which took considerable optimism since all three sectors have been at historic lows in recent years in that South American nation of 25 million people.

Besides its controversial record on human rights violations, Argentina's economy was in such chaotic state that despite tough measures begun in 1976 under its military junta, inflation is 84 percent. In one year, prices doubled and 20 banks folded, and grain and meat exports, the mainstays of its foreign exchange, are down 30 percent.

"I'm very bullish on the Argentine economy," said Luther Hodges, Jr., former undersecretary of commerce under Carter and now chairman of the National Bank of Washington. Last year he led a delegation to Argentina in what was interpreted as a softer new stance toward the country.

Even with its human rights problems, hodges said he thought then that Argentina had made dramatic progress and that the United States should do business with it.

The ambassador noted that Chase Manhattan Bank has been doing its part. David Rockefeller, the bank's retiring chairman of the board, "is really a good friend of ours," said Espil.

Bill Butcher, Espil's guest of honor who will become board chairman in April, put it a little more succinctly: "We're an important lender to Argentina. And I feel that under the leadership of President Videla and the minister of economics they have made tremendous strides."

If anybody had botched things, Butcher went on, climbing the stairway to the dinning room on the second floor, it was the United States which "failed as a nation -- Argentina had to face what amounted to a civil war and I'm respectful of what they've tried to do.

"From the standpoint of human rights," Butcher continued, "we have to recognize whose human rights: 15,000 terrorists killing people or 25 million peace-loving Argentinians wanting to get on with a tranquil existence?"

Over dinner of pate -- served from silver platters holding blocks of ice lighted from within -- roast lamb and baba au rhum, the discussion went on among the guests who included the ambassadors of Mexico, France, Saudi Arabia and Switzerland, Chase Manhattan board members William Coleman and Kimball C. Firestone, Allis Chalmers board chairman David Scott, Bendix Corp., vice president Nancy Reynolds, Union First National Bank's Richard Barrett, the Madison Hotel's Marshall Coyne.

"One of the nicest things about being a banker," Butcher said, raising his champagne glass in a toast, "is we tend to be with the nicest people in the world."

Whispered one guest later over coffee: "Whatever became of those 6,000 missing persons in Argentina?"