@qyanw35f explains this from a morphological perspective.
The characters 小 (small), 中 (middle), 高 (high), and 大 (big) each function as morphemes that carry their own basic meanings.
So, when broken down and translated literally, we get:
小学生 → small-student (elementary school student)
中学生 → middle-student (middle school student)
高中生 → high-student (senior high school)
大学生 → big-student (college or university student)
From the standpoint of word formation and morphological structure, this interpretation makes sense and is technically correct.
While I’m approaching this from a semantic perspective — focusing on the meanings of 小, 中, 高, and 大 within the context of the full words.
While these characters do carry meanings like "小small," "中middle," "高high," and "大big" as individual morphemes, in these compound words they are not referring to physical size or literal bigness. Instead, they indicate levels of education.
Specifically:
小 refers to the elementary school level
中 refers to the middle school level
高 refers to the senior high school level
大 refers to the college or university level
In this sense, these terms reflect educational stages within the school system.
Therefore, the "大" in "大学生" doesn’t mean "big" in a physical or literal sense — rather, it functions as a marker of higher education level.