They did not want to share political and economic freedom with freed slaves.
While it was true that the cotton gin reduced the labor of removing seeds, it did not reduce the need for slaves to grow and pick the cotton. In fact, the opposite occurred. Cotton growing became so profitable for the planters that it greatly increased their demand for both land and slave labor.
Out of the three movements, the independence of India was the one that required the least amount of fighting. India achieved its independence in a peaceful manner through the adoption of the ideas of civil disobedience. However, although the process of independence was initially peaceful and led to a straight-forward retreat of the British, its aftermath was more complicated. In the aftermath of independence, India was fragmented into India and Pakistan, with Bangladesh separating from Pakistan later on.
In the case of Latin America, there were several movements that took place at different times. However, several of this were unified thanks to the figure of Simon Bolivar. The conflicts that took place were a lot more violent than those of India. Moreover, fragmentation was also more significant, as these resulted in the creation of several new countries.
Finally, the independence of the United States took place much earlier than these other independence movements. The independence of the Thirteen Colonies was one of the earliest movements for independence to take place. However, it did not lead to the creation of a country. Instead, it led to the creation of a union or a confederacy of several separate colonies, united through some common ties and documents, such as the Declaration of Independence and the Articles of Confederation.