Sure. He ran as a sitting president and declined to run the second time. Fact is: he ran as a sitting president.
Also, other than him, who didn’t run as a sitting president: Let’s look at the last 100 years or so. Hoover, FDR, Truman, Eisenhower, LBJ, Nixon, Ford, Carter, Reagan, Bush Senior, Clinton, Bush Junior, Obama and Trump. Every single one of them ran for reelection. Why should Biden be an exception?
Trump ran when Covid was raging. Carter ran when inflation was double digits a and after the Iranian Revolution. Truman ran in 1948 when he was supposed to lose to Dewey (remember the infamous headline at the Chicago Tribune: Dewey Defeats Truman), etc. Sitting presidents run for reelection. It’s just how it goes and how it has been going for decades.