As the Constitution doesn't explicitly address the topic of education, decisions around educating America's children are (mostly) left up to individual states and territories. Which is to say, there isn't a "US education system", per se. Instead there are a handful of federal laws and acts that shape education (such as the 1975 Education for All Handicapped Children Act - now known as the Individuals with Disabilities Education Act, which requires public schools serve all children, regardless of disability status) but mostly there are 50+ different systems, each with their own history.

That said, there are some organizing principles that can help shed light on your question. First, many of the advocates of public education during the mid-1800s were inspired by what they saw in Europe, most notably Prussia. The ideas they brought back included setting up tax structures, grouping children by age, the professionalization of the teaching force, and ways to create an educational bureaucracy. Those advocates, such as Horace Mann, used those ideas to establish "common schools." The concept of "common" spoke to creating a shared school experience for all children, regardless of class (by which they meant white boys, and also their sisters, rarely Black, Asian, Hispanic, or Indigenous children). The curriculum of those schools, though, was very much organized around American principles - the idea of being a good citizen and good American. In other words, the American education system evolved into one that has an open-ended approach to a child's future. As a frame of reference, Prussia's system involved into one where children are "tracked" into different career futures.

In the context of curriculum, liberal (or modern) is a contrast to a classical curriculum (with a focus on Latin, Greek, rhetoric, math, and sciences) or a vocational education (more on that in a bit.) Between 1780 and 1880 or so, America slowly transitioned into a more liberal approach. School leaders advocated, that in order to be a well-rounded, informed adult citizen, children should study a little bit of a classical language, a modern language, math, English literature and prose, history, sciences, music, and physical education. To speak in broad terms, the general sentiment of American education was unconcerned with what careers or future a student might have; educators were responsible for sending them out into the world as well-rounded, as smart, and as citizeny as possible. (This is also tied up in the American notion of meritocracy and deeply linked to institutional sexism, racism, and ableism but that's beyond the scope of your question.)

Part of the reason school was focused on generalities more than specifics was because school didn't become a thing children were expected to do all day, for most of the year, until well until the 1900's. High school didn't become the norm until the 1950's and in some cases, states allowed children to leave school - for any reason - at 15 or 16. In effect, this means the notion that school is also about preparing children for what happens after school is relatively modern history in America. We can see early seeds of this idea, though, in east coast schools, especially New York State, which started to offer high school exit exams in bookkeeping, agriculture, auto mechanics, and home economics for students in the 1930's. Large cities began to open "specialty" high schools that offered electives or a vocational curriculum for high school students who knew what they wanted to do or didn't see a need for an academic heavy curriculum. In some cases, the demand came directly from parents - that is, rural parents would advocate their board of education offer courses on agriculture, animal husbandry, or carpentry. Some states created intermediary systems to run and staff regional schools that were (are) open to students from multiple districts. These schools emerged in most states in one form or another, and almost without exception, are based on the notion of individual choice - a student (or their parent) elects to attend such a program, with a liberal arts, academic-focused high school always available to them as the default. Meanwhile, some states or districts have created truly vocational high school settings - that is, everything a child does upon entering said high school is in service to what they might do after graduating. Early models (1960's or so) had students taking science classes in hospitals, or doing internships part of their day. Even those schools, though, maintained a liberal arts core; vocational education filled in the space or explicitly worked in the core subjects.

Finally, it should be noted that most states do require schools provide some form of civics or political education and financial literacy as well as sexual and media literacy education. But again, thanks to the 10th Amendment, the nature and structure of what that looks like in each state or territory is vastly different.