The U.S gained control over the Island of Iwo Jima and Okinawa because it wanted to get a clear position for bombing assaults on the Japanese home. From this position, the Japanese had the advantage of a clear path that could intercept American boomers route to Tokyo. In addition to that, capturing Iwo Jima provided the U.S with a point for emergency landing and refueling with an additional base from where fighters were escorted for the B-29 bombers.