Step into the wayback machine with me. Up until the mid to late-1800's, formal education on American soil for sons of those in power (which is to say, white men) generally followed what was known as the Classical Curriculum. While a boy would learn to read and write and basic arithmetic from his nanny or nursemaid, once he started worked with a tutor, it typically became a steady diet of Greek, Latin, some sciences, some math, rhetoric, and philosophy. Things like literature, history, and modern languages such as French, Spanish, Russian, Arabic, etc. would be relegated to his free time or case by case with his tutor. The colonial colleges (an answer to a previous question on admission to the colleges) expected mastery of Greek and Latin as evidence of intelligence, and as such, as long the boys who were educated in a classical curriculum grew up to become the men who led education systems, colleges, and write laws, it would endure.

There was, though, a massive sea change beginning around the time of the Civil War. The first shift was the rise of public (or common) schools. Numerous founders were advocates of the idea of government-funded schooling but their ideas didn't really get any traction until the 1840's or so. A whole bunch of factors came together to contribute to the shift: men of means became less resistant to the idea of paying for other men's sons education, social norms around the idea of "Republican Motherhood" loosened enough that (single) women could step out of the home and work as teachers without paying a social cost, and the notion of what was worth teaching and learning started to transform.

Learning things smart men knew was the norm for several generations. To be sure, no one learned Latin because it was useful; they learned Latin because smart men knew Latin and learning Latin made one smart. It was the prevailing understanding that this smartness enabled them to pick up the other knowledge they needed - politics, religion, the law, etc. Learning Latin, though, didn't necessarily make one a good American. The general consensus was that good Americans+ were industrious, pious (Protestantly speaking), and had the literacy skills necessary to be an informed voter. Beginning during Reconstruction, school advocates began to push for a more modern (sometimes known as English) curriculum. Part of this was practical. Getting more bodies into to the schools meant more teachers and training young women to teach Latin and Greek wasn't going to happen for a whole bunch of (sexist) reasons. This doesn't mean the languages went away - far from it - but rather, slowly, over the 19th century, history, literature, and modern languages were shifted from being being also-ran topics to being as important as Latin and Greek.

Around the end of the 1800's, the men running colleges, school systems, etc. etc. reached a frustration point around the quirkiness that made up American education. As an example, young men attending a high school in New Jersey in the late 1890's had a hard time getting into Harvard because their high school Latin teacher focused on the Latin texts Princeton expected for admission. There was a growing sense that there was need to smooth out some of the quirks and arrive at a shared understanding of what schools should teach. So, a group of about 90 members of the National Education Association (all white, all men) spend time surveying schools across the country and took stock of what was happening. From their survey, they pulled together recommendations. Their report called the Report of the Committee of Ten on Secondary School Studies, With the Reports of the Conferences Arranged by the Committee was published in 1894.

From an older answer:

There were four committees devoted to language: Latin, Greek, English, and Other Modern Languages. When they released their report, the language committees recommended that:

• students should start learning Latin in primary school
• Greek should be taught alongside Latin
• English grammar should be explicitly taught from a child's first day of school and English literature should be studied in secondary school
• students should start studying German or French around their 5th year (10 years old)

The reports also did something interesting regarding modern language - they advocated for teachers explicitly trained in teaching German or French. That is, they acknowledged that the pedagogy for teaching a new language is unique and should be treated as such. While they weren't the first to propose the idea, the Committee of 10 formalized the idea that teaching training needed to be specific, not general, and they used foreign language instruction as an example of why it was necessary.

However. If there's one thing that locked foreign language class into place, it's most likely the Carnegie Unit. In 1905, Andrew Carnegie announced he would fund college professor's retirement provided the college met his criteria for what counts as a college. It's worth noting that the country around this time was becoming consumed by the idea of scientific management; looking at a problem and breaking it down into smaller units was seen as a thoughtful, helpful, and ideal way to find a solution. This sentiment (which influenced every aspect of society - not just factories and schools) lead the Carnegie Foundation to think about education in credit hours. That is, a college was considered a college if their students met particular admission criteria (among other criteria). The Foundation looked at what the Committee of Ten recommended: "four years of English and a foreign language, and three years of history, science, and mathematics" and adopted it as their criteria. In other words, colleges wouldn't accept students if they didn't have all of the necessary units for admission.

Eh voila - foreign language class became a given in the American high school. As the criteria didn't mention a particular language, states and districts could determine which languages were taught. In the 1930's, students graduating from NYS high schools could take Regents exams in Hebrew, Latin, Greek, Latin, French, Spanish, or German. Other states offered Polish, Russian, Sign Language, and even Esperanto.

There are two additional things to stress. First, your exposure to a non-English language as part of a modern curriculum isn't about developing fluency. To be sure, developing fluency is a great side effect. Rather, the shift that I described earlier related to the shift in what it means to be a "good" American. Industriousness was still a key attribute - but so was the idea of potential and meritocracy. That is, American schools became about taking any child who walked in the door and setting them onto the path to prosperity and potential. Any boy could become a tycoon of industry or president. Any girl could become the wife of a tycoon or a president. A black child could work for that tycoon. (I'm being only mildly tongue in cheek - the roots of institutional racism, sexism, and ableism go deep in American education.) So the goal was to give students a rich, liberal arts educational experience that would expose them to lots of ideas and abilities, enabling them to create a future of their own choosing. (This stands in contrast to, for example, the German education system which tracks students into different high schools based on aptitude.) The notion of what's "practical" for students remains one of the great battles of American education.

Second, Spanish may feel like a modern introduction to the curriculum but it's been around in American schools for generations. From the Committee of Ten report on modern languages:

23. The recommendations we have made for French and German apply also to Spanish and to any other modern language that may be introduced into high or grammar schools.

New York State was offering a high school exit exam in Spanish in the 1920's and there were Spanish language textbooks from that period.

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+Not to put too fine a point on it, but again, the focus was white boys. Their sisters were more likely to go to school - white girls have always outperformed boys at school - but their educational needs were about their future as wives as mothers. The history of the education of Black children, once it was no longer illegal, followed a similar evolution from classical to modern, especially for children from families of means. However, several Black only schools across the east coast maintained a classical curriculum until well into the 20th century, most notably Dunbar High School in Washington D.C.