Gallup has a pretty cool interactive graph that follows presidential approval ratings.
It seems that while Truman's approval rating began pretty high at 87% at the end of World War II (which is understandable), it was completely in the shitter by 1952 when he was about to step down and hand over the keys to Eisenhower.
Why did more than 3/4 of the country hate Truman by the end of his term? I've only heard good things about him in history books.
The Fall of China set off a spiral of events that seriously injured his public approval ratings.
In August of 1949, the Truman administration published the “China White Paper,” which explained past U.S. policy toward China based upon the principle that only Chinese forces could determine the outcome of their civil war. Unfortunately for Truman, this step failed to protect his administration from charges of having “lost” China. The unfinished nature of the revolution, leaving a broken and exiled but still vocal Nationalist Government and Army on Taiwan, only heightened the sense among U.S. anti-communists that the outcome of the struggle could be reversed. The outbreak of the Korean War, which pitted the PRC and the United States on opposite sides of an international conflict, ended any opportunity for accommodation between the PRC and the United States.
The fall of China and the increasingly perceived threat of international communism led to heightened fears of foreign infiltration of the State Department. Senator Joseph McCarthy famously declared that there were at least 205 communist infiltrators in Truman's State Department. Truman's Justice Department did prosecute a large number Communist Party members, but resisted some of the broader programs advocated by McCarthyists in the legislature.
In addition to the crisis posed by anti-communist hysteria, The Korean War's prolonged stalemate opened him to a series of domestic issues that further marred public opinion of his office. The war caused high inflation and stagnating wages in industries key to mobilization. The United Steelworkers of America, in an effort to negotiate for higher wages, coordinated a national steel strike in 1952. In response, Truman issued an executive order seizing the national steel industry, which was ruled unconstitutional in the landmark Supreme Court decision in Youngstown v. Sawyer. If you zoom in on the graph OP posted, you will notice that this event (which took place in April 1952) actually corresponded with an uptick in Truman's approval, from 24 to 32 percent, and thus is not a likely factor in his low approval.
At around the same time, General Douglas A. MacArthur, a man lauded by most Americans as a hero for his leadership in the Pacific, was making overtures to expand the Korea conflict into an invasion of China and complicated Truman's efforts to negotiate peace with China. Truman relieved MacArthur of duty in April 1951, a decision which upset the public greatly. In General MacArthur and President Truman, Truman's mistake is explained as being
not the dismissal of MacArthur, but rather was, "a failure in political education. He made all the necessary decisions with great and simple courage; but he lacked the gift of illuminating them so that the people as a whole could understand their necessity." (ps 248-249).
In the 1952 Election, Eisenhower successfully seized upon public perception of Truman's faults (and by extension the faults of the Democrats), in his campaign strategy called the K1C2 formula. Instead of directly challenging his opponent, Adlai Stevenson, Eisenhower targeted Truman's three greatest weaknesses in the public's conscience: Korea, Communism and Corruption.