There are a couple reasons the US mostly used OD clothing during the war (Note: MOSTLY).

In the late 1930's, the War Department was still reeling from the aftereffects of the great depression, and military development in 1930's America was focused primarily on the funding and production of more modern firearms, such as the M1 rifle. In 1939, the Army numbered only around 180,000. Thus, it was more cost effective, as OD cloth was a lot cheaper to produce than multi colored cloth for camouflage. Also useful was the fact that once uniforms faded, they became a muted drab brown/green color that fit in fairly well with background colors. The US did issue camouflage uniforms, though. In 1940, the US Army Corps of Engineers experimented with camouflage uniforms, including modified versions of German "splittermuster 31" and Italian "Telo Mimetico" patterns.

In 1941 and 1942, after reports came, both from survivors of the Philippines and from Marines and Sailors on Guadalcanal of tan uniforms being terrible camouflage in the green hell known as the Pacific jungle, the Department of the Navy developed a "frog" camouflage known as P42. P42 was a two tone, reversible uniform of the same make as the P41 utilities issued on Guadalcanal. The first major use of the P42 uniform was in the later parts of the campaign in the Solomon Islands, and saw use in many roles throughout the Pacific. There were drawbacks to the P42, however, with the reversible fabric being too heavy for tropical use, and the tan fading to a pink hue. The helmet cover from the P42 found its way to the ETO, where it was used by Airborne Pathfinders during Op. Overlord, and later by recon units of Patton's 3rd Armored Division.

After the War, Camouflage uniforms fell out of use, with the development of the more modern M43 uniform. In the 1950's, the military attempted once more to produce a "leaf pattern" for use in subtropical areas, such as the Philippines and Cuba. This did not become widespread, and OD uniforms continued until the war in Vietnam. The French "Lizard" pattern was used up until the withdrawal of French Forces in Indochina. The newly formed Government of South Vietnam continued to use the "lizard" pattern for jungle and recon troops. After the US involvement in the war, advisors from the US and Australia began to use the lizard pattern, and adopted a modified "tiger stripe" pattern for use with recon and SF. The Tiger Stripe, as well as OD fatigues issued to average GIs was replaced in part by the ERDL pattern, developed in 1948 for use by the US. The ERDL evolved into the M81 pattern, the first widespread issue camouflage uniform for the US Armed Forces.

EDIT Sources: Grandfather was career Marine, Father career Army