Great Britain had a strong influence on America throughout 1700s & early 1800s. After 1812 war, British influence waned & they continued empire building. U.S. tended to not concern itself with rest of the world. If we were to assign a personality type to America from 1815 to 1895, it would be "introverted."
For 80 years America was self-absorbed & UK was growing their empire. A key ingredient in empire building was to project authority with a strong military. You need a large navy to mobilize your global hegemony; and you needed a big army to ward off anyone else coming around.
The British in the 18th & 19th centuries had much enmity for France. Germany, on the other hand, was literally part of "the family." The House of Windsor - British Royalty - had intermarried for several centuries with German Royalty - the Hapsburgs. Although the two families seemed to be great buddies - the political leaders of the countries kept a wary eye on empire building & the size of each other's army & navy. The two governments did not trust each other & regularly counseled their monarchs to exercise care; not be too open at the dinner table about their government strategies & secrets.
The British Empire's army and navy grew in the 19th century, which German politicians didn't like & regularly advised the Kaiser, Germany's navy was behind the British, and they needed to grow their navy to be able to keep UK navy in sight. Throughout the second half of the 1800s, America, no matter the topic, was not even close to either UK or Germany; especially not the U.S. Navy.
In the late 1870s, German politicians convinced the Kaiser to beef up the navy & the British Admiralty took notice of Kaiser's growing navy. The world's first arms race was on! The winner is the one with the biggest ships, and with the biggest guns. This continued into the 1890s and the age of the Dreadnaughts was here. Germany and Great Britain each wanted the biggest and most battleships - called dreadnaughts. This high stakes game of biggest navy started the two countries down path, so in 15 years it would be war and no longer a game.
In the late 1890s William McKinley became president, and was was pro-military. He appointed his new Cabinet, but his Navy Secretary didn't know much about running a navy; so there were many department duties he gave to his deputy secretary - Teddy Roosevelt.
Teddy paid attention to Germany & UK. He determined the U.S. Navy needed to begin adding ships. As President, he continued to build navy & had large fleet sail around the world as power projection.
In WW I, German & British navies fought with their battleships, with Germany winning most of them. When WW I ended, the German navy was captured & scuttled. Many treaties signed to limit navy sizes & quantity of ships. Germany, US & UK looked for ways around the treaties. UK still had biggest navy & didn't do much. Germany decided to make submarines & US did like Japan - build aircraft carriers.
World War 2 determined which strategy was right. UK's battleship navy wasn't right, as most of it was sunk. Germany's subs seemed right for awhile, until U.S. carriers sank most them. US carriers beat Japan's carriers. US proved to British that success is not about size or having most; its innovation & adapting. UK wanted keep empire, without changes.