Cadets is a popular activity among youth in the UK. There are Combined Cadet Forces in many prestigious boarding schools. Why are there no cadet programs in American private schools? Why isn't there more organizations like these in America? Are American youth different? I enjoyed my time in the Air Training Corps. I got to experience amazing adventures. I loved marksmanship and fieldcraft. I have been told that some of the school administration in the US think that a cadet program would interfere with the sacred cow of athletics. It is a shame that not all youth in the US has access to a cadet program.

https://www.raf.mod.uk/aircadets/

https://armycadets.com/

http://www.sea-cadets.org/

I joined the ATC before joining the RAF, 1288 Enfield Squadron, which sadly closed down many years ago. Summer camps were great fun.

I became an Army Cadet Force instructor after leaving the Royal Military Police, the senior officers in my county force disliked the ex regular instructors as we told the cadets, (who were hoping to join the forces when they were old enough), what to expect. They were the ones who knuckled down in lessons to absorb everything we were teaching them. I preferred teaching a class full of cadets like that instead of the ones who only turned up to be disruptive.

There are cadet programs in American schools.
Reserve Officers Training Corp, R.O.T.C. is active at the college/university level. At the high school/middle school level there is Junior ROTC. All branches of the U.S. Armed Forces support JROTC, although the Army is probably the most prevalent.
JROTC was established by the U.S. Army at the high school level in the 1930s when it was apparent that the U.S. would be involved in a major war requiring a vast expansion of the Army. While senior ROTC in colleges and universities would provide officers, JROTC was designed to train future non-commissioned officers at the squad leader / assistant squad leader level. The training program was quite comprehensive and involved all the usual basic military skills.
JROTC continues today. There are private military academies at both the senior ROTC level, ( such as Norwich) and at the JROTC level. However, the emphasis in schools now is on using the program as a citizenship course rather than as a military manpower source. The U.S. Forces are now all-volunteer and have good success in meeting manpower needs, so they don't need vast numbers of people.
Frankly, in some places there is an anti-military bias among the citizens and JROTC is not as big a program as it once was. In places where it is established in high schools, such as Long Beach, California students must take either Physical Education or JROTC.
I was a volunteer rifle instructor in one of the Long Beach high schools in an Navy JROTC unit. The unit had three full-time instructors who were retired Navy officers or petty officers. I volunteered to teach air rifle one day a week. We had a portable air rifle range and Daisy target rifles.
The students competed against other school JROTC units in sports, drill and marksmanship. So, I'm sure it's similar to cadet programs in the U.K.
There are also cadet programs run by the Navy League ( Sea Cadets), the Air Force has the Civil Air Patrol, the Marines has a couple of programs, ( Devil Pups). All branches of the U.S. Armed Forces strongly support the Scout movement.

Because in other nations cadets is a legitimate youth hobby. In the US cadets are used as an recruitment tool.