Answer by taking a quote from the following article:

David Monroe Shoup (30 December 1904 - 13 January 1983) was a decorated general of the United States Marine Corps who was awarded the Medal of Honor in World War II, became the 22nd Commandant of the Marine Corps, and, after retiring, became one of the most prominent critics of the Vietnam War. Born in Indiana to an impoverished family, Shoup joined the military for financial reasons. Rising through the ranks in the interwar era, he was twice deployed to China during the Chinese Civil War. He served in Iceland at the beginning of U.S. involvement in World War II, and as a staff officer during the Pacific War.

In mid-1943, Shoup was transferred to the staff of Major General Julian C. Smith, commander of the 2nd Marine Division, and tasked to help plan the invasion of Betio on Tarawa Atoll. Shoup's aggressive leadership style would complement the offensive strategy his superiors were seeking in taking the atoll. He was tasked with drawing up initial plans, designating the landing beaches on Betio for the 2nd Marines, and overseeing some rehearsals at Efate. However, after Colonel William W. Marshall, commander of the 2nd Marines, suffered a nervous breakdown before invasion, Smith promoted Shoup to Colonel and gave him command of the regiment, in spite of Shoup's lack of combat experience.  The invasion commenced on 20 November 1943, with Shoup disembarking from Maryland, the flagship for the invasion. His force met heavy resistance on the beaches. His LVT was destroyed by shore fire, and he had to proceed without transportation. As he was wading ashore at around 11:00, he was struck by shrapnel in the legs and received a grazing wound from a bullet in the neck. In spite of these wounds, he rallied the Marines and led them ashore. He was able to coordinate the troops on the beaches and organize them as they began to push inland against an anticipated Japanese counterattack. He continuously organized aggressive attacks on the defenders, and was noted for his bravery and vigour during the conflict. On the second day of the attack, he organized an advance inland, despite heavy casualties among the American troops. By the afternoon, they were winning the battle, and reinforcements began to arrive in force. That night, Shoup was relieved by Colonel Merritt A. Edson, the division's Chief of Staff, who commanded the 2nd Marines for the remainder of the campaign. Six years later, Shoup made a cameo appearance in the movie "Sands of Iwo Jima" reprising his actions that first night on Tarawa, although he had originally been brought onto the movie as a technical advisor.  For his leadership during the assault and the push inland Shoup was awarded the Medal of Honor and the British Distinguished Service Order. For his role in planning the invasion he was awarded the Legion of Merit with "V" device. He also was awarded the Purple Heart for the combat wounds he suffered during the course of the campaign. Ten years after the assault, Shoup remarked of the operation, "there was never a doubt in the minds of those ashore what the final outcome of the battle for Tarawa would be. There was for some seventy-six hours, however, considerable haggling with the enemy over the exact price we would have to pay." In 1968, he returned to Tarawa to dedicate a memorial to the battle and to the American and Japanese troops who had died there.

Why was he relieved that night instead of waiting?
he was struck by shrapnel in the legs and received a grazing wound from a bullet in the neck.