Why did the US have a plan for the event of war against Britain in the 1920s?

This paper goes into detail about the war plans of both the British and the Americans. It's quite readable, and if you're interested, I'd suggest taking a look.

For the question itself: interpreting your question as if the US and UK are friends, why bother planning for a war against a friend?, then you'd be right, most of the time both sides thought it was unlikely to go to war with each other, but they thought about it anyway in times of crises. After all, even if you know for sure that you will not resort to force, can you say the same of your erstwhile ally?

The plans of the US and British navies for an Anglo-American war have received little attention because most historians accept the premise that such an event was 'unthinkable'; that the likelihood of war between the United States and the British Empire was so remote as to have become an absurdity. For planners in the armed services, however, who accept as a matter of course that states use force whenever necessary to further their interests, it was natural to assume that any other state would, in certain circumstances, resort to war. And while it is true that British and US statesmen did not rate highly the likelihood of war between their two countries, in moments of crisis their thoughts turned to the possibility. No less a figure than Winston Churchill, the architect of the Anglo-American 'special relationship' and, after 1963, an honorary American citizen, could write in 1927 that although it was 'quite right in the interests of peace to go on talking about war with the United States being "unthinkable", everyone knows that this is not true.'

A second reason is that, no matter how unlikely, if there were a war, the consequences would be dramatic. Think about why people buy insurance for example - sure it's unlikely that your house burns down, but if it does, can you afford to be uninsured?

The consequences of the outbreak of war were potentially so great that no responsible decision-maker could afford to dismiss the likelihood out of hand. Americans feared that war with the British Empire might lead to the destruction of the US fleet and the temporary interruption of US overseas trade; to attacks on major industrial centres by British air forces based in Canada; and to the invasion of the continental United States by an imperial army drawn from Britain, Canada, and the other British colonies. For Britain, the results would be just as damaging and much more probable: the destruction of the British fleet, the conquest of British colonies and former colonies in the western hemisphere, the disruption of Britain's overseas trade, and, in the event of defeat, an immense blow to British prestige. Although each of the two assumed that it would never start the war, each also knew that it could not predict the other's conduct with certainty.

Finally, war planners keep "in shape" by planning for war. They are more familiar with what assets they have, what (natural) obstacles they might have to deal with, how long it takes to deploy ships from the Pacific to the Atlantic, and so on:

Indeed, it has been suggested that the 'essential value' of the US naval war plan against Britain - Plan Red 3 - 'was to accustom service planners to dealing with the complexities of an Atlantic centered conflict'

You'll find more examples later in the document. For example, British war planners thought about the threat of the US moving a fleet from the Atlantic to the Pacific, via the Panama Canal. This is not just dangerous to British trade, it might have led to the capture of some colonies such as Hong Kong. As a result, British planners thought about capturing the Philippines to deprive the American navy of bases. Either way such a war is going to be complex, and of course, when it's complex, it's necessary to think about it.

The US Navy developed plans for a naval war with Great Britain for several reasons:

1. The US had been to war with GB on multiple occasions.
2. The Royal Navy was the largest navy in the world.
3. If the US Navy was built to defeat or significantly damage the Royal Navy they could take it as a given that they could take on any navy in the world on, at worst, equal terms.
4. The US Navy also had to be able to counter the growing threat posed by the Imperial Japanese Navy, and thus needed to be large enough to fight a "two-ocean" war simultaneously.

Thus the US Navy was not just concerned with a battle in the Atlantic vs. the Royal Navy - it also was concerned that it would have to fight a simultaneous battle in the Pacific against the IJN.

It was not until the Great Depression that this doctrine changed. Prior to his service as Chief of Naval Operations (CNO) Admiral William Veazie Pratt served as part of the US delegation to the London Naval Conference, where he became personally familiar with the men in charge of the Royal Navy from both a military and civilian perspective. When he became CNO in September of 1930 Admiral Pratt recognized that although the Royal Navy was the largest fleet in the world the political realities had changed. America and Great Britain had become long-standing and close allies, and Great Britain and the Royal Navy thus no longer posed a threat to the United States. As such, priorities were shifted. The assumption was made that the Royal Navy would take principle responsibility for fighting in the Atlantic and the Mediterranean, while the US would take principle responsibility for fighting in the Pacific, and that the US Navy could thus be sized appropriately for a "one ocean" war.

I served briefly aboard USS William V. Pratt (DDG-44) as a 1st-class midshipman during the summer of 1978, and so became acquainted with Admiral Pratt's contributions to the US Navy.

Britain was formally allied with Japan. And a war with Japan could theoretically lead to war with Britain. This could happen, for instance, with regard to U.S interests in Asia, particularly China. The U.S. supported an Open Door Policy in that country, the other two did not.

America had gone to war with Britain in 1812, and "come close" several more times in the 19th century.

But it was mostly a "wargaming" exercise to test the 5-5-3 ratio naval tonnage ratio for the U.S., U.K., and Japan, and the impact of the U.S.'s 5 versus the other two's 8.