Question:
what were the reasons for fighting on these islands too?
please explain how progressed?
Answer:
An island provided whoever possessed it with an unsinkable, if somewhat immobile, aircraft carrier. Airplanes from these and naval aircraft carriers could control the shipping lanes for hundreds of miles around them, which ultimately threatened the supply lifeline between the United States and Australia. Australia at one point, of course, was threatened with invasion, and Australian units were heavily involved on islands north of the continent, especially New Guinea, on which there was extremely heavy fighting rarely reported here.
In the summer of 1942, the Japanese army began building an air strip on Guadalcanal, which would have extended Japanese control further south from Japan's major base in the area at Rabaul. American Marines interdicted this effort by invading the island and capturing the airstrip, making it one of ours. This led to months of bitter fighting when the Japanese tried to recapture the air strip.
From there, the U.S. moved up the Solomons "Slot" toward Rabaul, which never was captured but was neutralized and bypassed. Ultimate goal was recapture of the Philippines, which had belonged to the United States from the time we took them from Spain in 1898 to the time Japan captured them early in 1942.
The Japanese also established a monster base at Truk in the Carolines, from which it radiated satellite bases. Japan had been ceded the Carolines and the Marshalls after Germany's defeat in WWI. Early in the war, Japan captured Guam, also an American territory, and it tried to capture Midway but was defeated in a major naval battle which became the turning point of the war.
The United States commenced an "island hopping" campaign in the Central Pacific when it invaded the Tarawa atoll in November 1943. Additional islands were captured subsequently -- Einiwetok, Roi-Namur, Saipan, Guam (we got it back), and eventually Iwo Jima and Okinawa (all with the same objective, which was to roll back Japanese air power while establishing our own). Capture of Saipan and Tinian made it possible for America to bomb Japan, itself, once the B-29s began coming online. The Americans had had a plan before the war to bomb Japan in the event of war, using shuttle flights of B-17s from the Philippines through to Siberia; however, the Soviets refused to declare war on Japan until the very end, and this had deprived us of use of their territory. Prior to late 1944, except for the single Doolittle raid from the aircraft carrier Enterprise, America had been unable to take the battle to Japanese military and industrial facilities in Japan because of the distances involved.
The British as such were occupied primarily in India and Burma, and as far as I know, major British units did not participate in island battles other than any islands contingent to northern India and Burma. There were British plantations on some of the Pacific islands before the war, and Americans were aided by groups of British "coast watchers," especially during the campaign in the Central Solomons. The coast watchers, however, for the most part were civilians who just wanted their farms back.