Well, maintaining a large fleet of aircraft carriers has distinct requirements and serves distinct purposes. While other powers have dabbled in carrier fleets, only the US is truly compatible with both sides of that equation.

Carriers have been the gold standard of naval power since WW2, offering top-level abilities to project power globally and control the open seas. They are also hugely expensive, and require large commitments of infrastructure and resources. In order to make any usage of carriers make sense (not a mere token carrier or two) the nation in question would have to have the resources to support a large carrier fleet and the logical strategic need to do so.

The US is a traditional naval power, protected by oceans and distance from the centers of power and conflict in the world, and possessed of a wealthy and technologically advanced economy. The US can afford carriers, has the tradition and infrastructure to use them effectively, and carrier fleets suit their strategic situation. Motive and opportunity dictate the outcome here.

Now compare that to the other main powers of the post-WW2 world. The USSR had the size and economic base to possibly field such a fleet. However, their strategic situation rendered carriers somewhere between a luxury and a waste of resources - their strategic priorities were fighting land wars against close-by neighbors (NATO or China, mostly). They needed tanks and aircraft, which they had in droves. Carriers, while nice, would not have helped much deciding land battles in Germany or Manchuria, and the resources necessary to make an effective carrier fleet would have been much more effectively used on more tanks or planes. They had the theoretical potential to field a carrier fleet, but no particular need compared to the cost.

The other main powers all follow similar patterns of failure of capacity or need:

Britain - Could use such a fleet, and attempted to maintain one for a while, but postwar Britain simply couldn't afford it.

France - Similar lack of capacity, but less of a need.

China - Some need, but only now beginning to develop any capacity.

India - Some need, modest capacity at best.

And et cetera all the way around. In addition, NATO and western countries could call on the help of America's carrier fleet when needed, so why buy the cow when the milk is free? In the modern world, only the United States has traditionally had both the need and the capacity to maintain a large carrier fleet. China may be joining them, but has a long way to go to match the US in capability should they even decide it makes sense to do so.