AMERICANS WILL almost always encourage someone to move out of his class, but not out of his category. Gen Tunney, the heavyweight champion who died last week, rose from poor boy to banker, with a socialite wife. That was all right. But as fighter Mr. Tunney was given to quoting Shakespeare, and he wasn't a slugger, and he quit the ring when there was hardly a mark on him. That was not all right. He looked like an actor; he sailed to Europe to talk with George Bernard Shaw, he did not act like a pug. The fans would not forgive him.

They took to Jack Demsey instead - Jack Dempsey, whom Mr. Tunney had whipped twice, who knew neither socialties nor Shakespeare, and had not the sense to go to a neutral corner in the legendary seventh round of their second match, but just stood there hulking over the graceful champ, as his title ticked away. That Mr. Tunney knocked Mr. Dempsey down in the very next round, and went on to a unanimous decision, would not be remembered. Something there was in Mr. Tunney that told the country he hadn't really earned his crown.

In a way, such thinking was understandable. Through the fight career, the Wall Street career, the Navy career - all successes - Mr. Tunney seemed born to his achievements, as if they had been foreordained.

On the contrary, Mr. Tunney had worked long and hard to get to be champion, had risen, in fact, through three weight classes; and when he framed his million-dollar check after the second Dempsey fight, it was less an act of flamboyance than proof of sweat. Yet most people would not see it that way. And Mr. Tunney wouldn't let them. It suited him to prance about, and shoot off his mouth too often, to bespeak both sides of the 1920s: the glitter and disdain.

If he had stuck it out as champ for more than three fights, he undoubtedly would have won the public's heart. Part of the popularity Muhammad Ali now enjoys is due to his having stayed around as champ, and eventually overcome the undeserved hatred he'd acquired. But Mr. Tunney was lighter on his feet, even than Ali. He had other things to do than fight, and so became a full-time public figure.

In the long run, of course, all was forgiven. In the 1950s and 1960s, he made all sorts of public pronouncements, and traipsed about Congress with Mr. Dempsey, his life-long friend, to argue for a national boxing commission. He had achieved the statesman's status, and the publice associated him less with his life than with theirs. So he died a hero. But there never was any real understanding of this man, who was too gifted, too fast and driven, to stay where the people wanted him.