In the late 19th century America built a modern fleet second only in the world to Britain's. This coincided with much warmer Anglo-American relations. However when Germany began a naval build up(albeit accompanied by belligerent actions against France) it was strongly opposed by Britain. Why was this?
"All men may be created equal, but not all ships are created equal." -- some old white dude
I'm going to be brief here, but what it boils down to is that the American naval buildup of, say, 1880 to 1914 or so occurred in an era in which America was generally interested in a coastal defense force (rather than an expeditionary force), and in which America was either a close friend to Britain, or at the very least not an enemy of Britain.
During that time the US fought one naval war, the Spanish-American war, during which the American navy's gunnery performance was utterly abysmal (but ever so slightly less abysmal than the Spanish), and during which the USS Oregon made its famous "dash" from San Francisco to Florida in 66 days.
Oregon and its two sister ships were coastal defense battleships, with a freeboard insufficient for much time spent in the open sea. The next 10 battleships the Navy built were also meant for coastal defense, with a relatively slow top speed and short range. It wasn't until the Virginia class, which only commissioned in 1906, that the U.S. had a truly oceangoing battleship, and the Virginia and ongoing classes were obsoleted by HMS Dreadnought. The South Carolina class was the first US dreadnought class, and they didn't commission until 1910; the US had 10 dreadnought battleships by the time the war broke out in 1914.
So, the short answer is that the US didn't have true oceangoing battleships before 1906, and didn't have dreadnoughts until 1910. The distance of the US from Britain and the amity between the two countries meant that the American threat to Britain was nonexistent. (Amity between the two is also helped by the fact that the US did not intend to build a colonial empire, in contrast to German ambitions.)
By contrast, Germany had, after the Franco-Prussian war, the largest army in Europe. Britain could deal with that though its continental allies, but Germany building a fleet to challenge the British fleet, combined with that army, would make Germany unstoppable. The German fleet was a direct existential threat to the existence of the British empire, and the British reacted accordingly.
Some reading on the period:
Robert K. Massie, Dreadnought: Britain, Germany and the Coming of the Great War: A naval-centered but wide-ranging story of the missteps, misunderstandings, and hubris that led up to the outbreak of World War I.
Robert K. Massie, Castles of Steel: Britain, Germany, and the winning of the Great War at sea: The follow-up volume to Dreadnought, which takes a global look at the British navy during World War I. Includes a very balanced section on Jutland which avoids some of the personality-driven history that has cropped up around the event.
Robert L. O'Connell, Sacred Vessels: The Cult of the Battleship and the Rise of the U.S. Navy: An examination of the power of the idea of the battleship and how it shaped and was shaped by Mahanian thought, leading to the development of the modern American navy. Also has interesting sections on asymmetrical threats to the battleship (planes, torpedoes) and how those were subverted or sublimated by naval thinkers.
(The quote at the top isn't a real quote.)
America wasn't a country with a military mindset that guided everything it did. Germany was, it was an every increasing economic powerhouse and had the largest professional army in Europe. Wilhelm II also wanted a Navy that would rival England's. Britain could easily put 2 and 2 together.
The US on the other hand was genuinely trying to guards it's trade and sea lanes, as well as the coasts etc.
The UK was wary of American Naval power being built up before 1812 for obvious reasons.