This tension within the government of the United States can be traced back to the creation of the nation. At the beginning of its history, the United States was a collection of colonies, all of which were considered independent of each other. However, as the colonies gained independence, they decided to join in order to be stronger and ensure more protection. This led to a loose Confederation, which was the first instance of a United States.
An example of this was the writing of the Articles of Confederation. These articles were written by delegates from each of the colonies that had recently gained independence. The Articles are considered the first Constitution of the US, and they gave the federal government very little power, allowing states to have most of it. The passage of the Constitution reverted this to some extent, giving slightly more power to the federal government.
Another example of this tension occurred in the early 19th century. During this time period, each state was able to decide whether they would allow slavery within their borders, without much interference from the federal government. With the passage of the Missouri Compromise in 1820, half of the states of the country were slave states, while the other half were free states. This tension led to the Civil War.
Finally, prior to the Civil Rights movement in the 1950s and 1960s, segregation and Jim Crow laws were common in many states of the South. Many of these states refused to accept the authority of the federal government when these practices were outlawed.
The founders of the nation most likely made this possible for two reasons. First, they wanted to allow the original colonies to retain some of their original sovereignty. Second, they wanted to prevent the federal government from having too much power, as they believed that this could lead to a second monarchy or a dictatorship.