Why Kissinger? That is the question that has preoccupied Washington since President Reagan announced last week that former Secretary of State Henry A. Kissinger was his choice to head the new bipartisan commission on U.S. policy in Central America.

The clue to this seemingly strange appointment cannot be found in the diplomatic record of Kissinger or the political past of Reagan. In the 1970s, Kissinger treated Latin America with the same disdain with which Reagan viewed Kissinger as a symbol of the snooty Establishment approach to foreign policy. But it becomes perfectly understandable if you just remember that the president is one of the great show business figures and fans of our time.

He knows what will work at the box office, and he understands that this is the year of revivals in Washington. The big hits of the Kennedy Center season were new productions of such golden oldies as "On Your Toes," "Show Boat," "Porgy and Bess," and "You Can't Take It With You." And the summer hit at Arena Stage is a revival of Leonard Bernstein's musical, "Candide."

What these splendid shows have in common is that they go back to the days when Ronald Reagan and Henry Kissinger were fresh faces. You don't have to be a licensed shrink to see how appealing the idea of reviving past glories might be to both of them.

If I had to pin down the birth of the Kissinger Commission to any one event, it was probably the publicity that flowed last December when George Abbott, the 96-year-old director of the original production of "On Your Toes," came out of semi-retirement to put the new version back on the boards. To George Abbott, Reagan and Kissinger are just a couple of kids, starting out their careers.

While the highlight of the show, George Balanchine's jazz ballet, "Slaughter on Tenth Avenue," may have unfortunate implications of a militaristic solution to the El Salvador struggle, the more pertinent example was the casting of Natalia Makarova as the classic ballet dancer who learns to swing.

Makarova has a Russian accent that makes Kissinger's Germanic pronunciation seem almost intelligible. No one understood a line she uttered on the Kennedy Center stage, but she captured everyone with her charm. Chances are no one will know what Kissinger is saying about Central America. But what an aura he will bring to the part.

Once the idea was planted, I think almost every new show that opened at the Kennedy Center gave impetus to the notion that was growing in Reagan's mind. Jason Robards came back in a revival of "You Can't Take It With You," with James Coco and Colleen Dewhurst supplying the exotic accents as Boris Kolenkhov and Olga, the former grand duchess fallen on hard times --a sort of Kissinger in drag. When Robards' pal, Mr. DePinna, chased the internal revenue agents out of the house with his homemade fireworks, Reagan must have seen how easy it would be for Kissinger to set off the verbal rockets that would rout the Sandinistas.

"Show Boat" and "Porgy and Bess" brought songs that just seemed to shout Kissinger's name. "Only Make Believe" was surely a reference to his famous "Peace is at hand" message from Vietnam to the American voters on the eve of the 1972 election. Three melodies from "Porgy" seemed to suggest the underside of the Kissinger reputation: "Here Comes the Honey Man." "I Ain't Got No Shame." And, of course, "It Ain't Necessarily So."

But for any who questioned the choice, Reagan had only to hum a few bars from the Kern-Hammerstein classic, "Can't Help Lovin' Dat Man."

Still, he hesitated a long time. Not until "Candide" settled in for a long run at Arena this summer did the decision become firm in Reagan's mind. The star of the show is Voltaire's hero, Dr. Pangloss. He is the eternal optimist who, while having his way with the wives, the purses and the honor of his gullible followers, keeps assuring them that by following his simple rules, they will learn that "all is for the best in this best of all possible worlds."

In the spirit of box office bipartisanship now prevailing, it would ill behoove me to suggest there is a direct comparison between the slippery musical hypocrite and the distinguished and now happily revived Herr Doktor Henry.

I will just say this: The last three songs in "Candide" offer a preview of the Kissinger Commission report and the future of American policy in Central America. "The Best of All Possible Worlds" is followed by "You Were Dead, You Know," and finally, a hymn to staying home, "Make Our Garden Grow."