Edit: I've added some headers and retracted factually incorrect information.
The Status of the Metric in the United States
Strictly speaking, the US has been "metric" since the Mendenhall Order, issued in 1893. The inch is defined as exactly 2.54 centimeters, the pound (mass) is exactly 0.45359237 kilograms, the pound force is exactly 4.4482216152605 newtons, and so on. The conversion factors have changed a bit since 1893, but that there are defined conversion factors has not.
That said, there's a lot more to "going metric" than having some conversion factors hidden underneath the hood. There's a whole lot more to "going metric" than changing our speed limits and highway signs. Printing 453.6 grams in small print after a bold 1 pound on a can of peas is not "going metric", nor is exchanging the order of those units on that can of peas. Printing the size as 453.6 grams in bold and 1 pound in small, parenthesized print also is not "going metric."
"Going metric" means changing the size of that can of peas to 500 grams or 400 grams and printing the customary units (which will now be oddball numbers) in parentheses. It means changing the size of wires from American Wire Gauge to the metric wire standard, changing the sizes and pitches of screws and bolts from nice even fractions of an inch to nice even fractions of a centimeter. "Going metric" means changing the manufacturing base, from bottom to top.
European Measurement Systems in the 19th Century
No answer has yet mentioned the chaos of measurement systems in Europe prior to the French Revolution. Different countries each had their own system of units, or worse. Oftentimes, towns separated by a day's ride had their own systems of units. It was chaos, and it was that chaos that the French Revolution tried to address. There were no standards prior to the French revolution. Continental European countries addressed this chaos by switching to metric units. Metrication in western continental Europe was largely complete by 1876.
Other countries addressed that chaos in less draconian ways. Industrialization in the United Kingdom mandated having a consistent set of units. The UK Parliament did consider converting to metric units, but eventually instead standardized the informal units used in slightly different ways across the British isles in the Weights and Measures Act of 1824. This act cemented the use of imperial units in the UK until 1965. It was this standardization that formed the basis for the goofy units still used in the US (and informally, still used in the UK).
No answer has yet mentioned the importance of centuries of war in Europe, culminating in the two World Wars. The two world wars wiped out the manufacturing base throughout most of continental Europe (and also Russia, Japan and China). They had to rebuild. The only system of measurements that made a lick of sense as the basis for that rebuilding was the metric system. Continental Europe was already metric. They weren't going to switch to the goofy British units.
It took those countries devastated by World War II twenty years to recover from the horrors of that war. The countries whose manufacturing base were not devastated? That would be the Commonwealth nations and the US. Manufacturing capabilities in continental Europe were bombed to oblivion during those wars, particularly during WWII. At the same time, the Commonwealth nations and the US underwent a huge build-up of their manufacturing base. This build-up was done using imperial units. There was a lot to lose in the Commonwealth and in the US by converting to metric. The Commonwealth countries were amongst the last to officially "go metric". The US? Not yet, but that too will come to pass.
The UK was the first of the Commonwealth nations to "go metric," and that only started to happen in 1965. By that time, 20 years after WWII, continental Europe had rebuilt their manufacturing base. Continental consumers liked having their cans of peas and all kinds of other consumer products expressed in metric units, and continental manufacturers liked having their screws, bolts, and all kinds of other industrial products expressed in metric units. UK manufacturers found themselves in the untenable position of maintaining two production lines, one based on imperial units for a small domestic market and another based on metric units for a potentially much larger export market across the Channel. The impetus for the British conversion to metric was largely industry-driven. The British people were steadfast against going metric; some holdouts still are.
Metrication in the United States
The US is a special case. No bomb were dropped on US cities, railway depots, or manufacturing plants during WWII. A large number of American soldiers did die in that war, but the US manufacturing base escaped the war unscathed. To the contrary! The US instead built up a massive manufacturing base during WWII. It was this build-up that resulted in the US being the world power after WWII. This build-up is also why the US has not yet "gone metric."
Unlike Great Britain, the US has a huge domestic market. Being attractive to that huge domestic market was key to survival for a US-based company for much of the post-WWII era. Exports? They were a nice add-on to the bottom line. Besides, for the first twenty years after WWII, what else were those outsiders going to buy other than American products? Europe and Asia had no manufacturing base. They bought American made products.
That calculus is changing. Just as it made no sense for UK-based manufacturers to have two production lines 50 years ago, it makes no sense for many US-based manufacturers to have two production lines now. If you own a recently built automobile, it will be metric through and through, It doesn't matter whether than car was built in Mexico, Canada, Europe, Asia, or Detroit. The US automotive industry has "gone metric."
That the US automotive industry has indeed "gone metric" will ripple throughout the US manufacturing base. This plus other aspects of globalization will eventually end the use of customary units in the US. The US will convert to metric units for the same reason the UK did: Those archaic customary unit make no sense from an industrial perspective.