Hall and Soskice's book Varieties of Capitalism lays out possible reasons. The part of the book that I have read references the strength of contracts in Germany. It's very easy to sign a worker and have her work for you for a long time, so you are willing to invest your own time and money into an apprenticeship program.

In the United States, anyone can hire or fire basically anyone. If I'm a firm thinking of starting an apprenticeship program, I have to worry that my competitor will offer my apprentice more money the second she is done being an apprentice, meaning I just wasted time and money.

This gives insight into why apprentice programs pop up in the United States. For example, the Newport News Shipyard, which is quite large, has an apprenticeship program that works quite well for them, probably due to the fact that their students learn specialized skills that would be hard to transfer easily into other jobs, and the fact that there really aren't many military shipyards left.

I hope this helps, maybe someone else can bring a more historical argument as opposed to an economic institutions argument.

Maybe an idea to include a link to such an article? That'd clear up the context a bit, whether we're talking about historic appprenticeships, or a modern apprenticeship system, or a connection between the two, et cetera.

I'd also offer the twin American strains of meritocracy and a public education system focused on the liberal arts (the classics).

Merit by Kett gets into how deeply ingrained the belief that anyone can become anything is in America. That thinking informed the NEA Committee of 10 in 1892 when they were making their proposal for the look and structure of American secondary education. Unlike Germany, which provides three (college-bound, professional, and trades) tracks for secondary schools ([source] (https://www.german-way.com/history-and-culture/education/the-german-school-system/)) starting at age 10, American secondary schools are generally structured the same; all students receive a comprehensive education which includes the arts, physical education, literature, mathematics, science, Social Studies and civics, and a foreign language.

There are some speciality high schools or vocational education programs but these are relatively new and mostly found in cities or larger districts.

Basically, Germany has a pipeline of young people ready to join trades and industry because they feed that pipeline starting when children are ten. America waits until children are able to make that choice from themselves as teenagers.