In 1960 the United Nation General Assembly adopted the UN General Assembly Resolution 1514 (XV), or the Declaration on the Granting of Independence to Colonial Countries and Peoples. Nine countries abstained: Australia, Belgium, the Dominican Republic, France, Portugal, Spain, South Africa, the United Kingdom, and the United States.
Why did they abstain rather than voting against it? Did they think voting against it would look worse than just refusing to vote for it?
It had to do with "prestige." In the Department of State Foreign Relations, United Nations and International Matters series (1955-57, 1957-59) there are a lot of published memos of this issue between Wilcox, Lodge, Dulles. From 1952 onward, ever since the Soviets began to push for decolonization among the colonies, the US and the old Administering Powers understood that they could not be seen as revoking the Sacred Trust of Chapter XI of the UN Charter, which would administer colonies towards self-government. It should be noted that all the Marshall Plan countries (aka Truman Doctrine), were also the same Administering Powers that listed their territories on the UN list of Non-self-governing territories (NSGT). The Marshall Plan was also the driver of the Cold War that undermined and betrayed the agreements originally established under the Yalta, Malta, and Potsdam Agreements between the US, the UK and the Soviet Union in regard to United Nations post-war planning.
The Soviet push for decolonization, was a logical departure from the language of "self-governance," and the US and old Administering Powers quietly rejected it. But as UN membership grew, the US understood that they could not reject it, and had to rather, abstain on technical measures, rather than be seen as rejecting it. Generally speaking, new countries would be more likely to side with the Soviet Union when it came to UN votes, since the Soviets had helped them become independent. In defense, the US had to ensure that they too would engage in "liberation" struggle so that the Soviets would not win every UN vote as a bloc. There were also other manipulations like giving Indonesia half of New Guinea (West Papua) in exchange for them to not trade with the Soviets.
Also because many of the Administering Powers still held their territories, the new States having had become independent with the help of the Soviet Union were in favor of UNGAR 1514, so when it was passed in 1959, it launched the decade of decolonization from 1960-1970 which saw the liberation of most of Africa and South East Asia. For much of the Pacific, their independence was gained in the 1970s and 80s. To note, Australia, France and the US still hold territories in the Pacific, despite decades of independence struggles.
When we think about liberation struggles in Vietnam, Cambodia, Laos, and Korea, these were the administering powers unwilling to let go of their colonial possessions.