Many people learn that sophomore means "wise fool." It is a neat description of a second-year student. It is also probably not where the word comes from.
The real root is the university debate. At Oxford and Cambridge, a student in the middle years was a sophister. Sophisters took part in dialectic exercises, the formal arguments at the heart of medieval teaching.
From the same family came sophume, an old variant of sophism, and from it sophumer, recorded in the 1650s. Etymonline glosses the later word as literally "arguer." The ending may have been modeled on agent nouns such as philosopher and sorcerer.
All of these go back through Latin to Greek sophistēs. It meant a master of a craft, or a wise and prudent man. The modern insult in "sophist" came later.
By the 1680s the form sophomore appears. Here the folk explanation enters. Greek sophos means "wise" and mōros means "foolish, dull." Read that way, the word describes a student newly sure of opinions he has not earned.
Etymonline treats this as a likely influence on the spelling, not the source. Merriam-Webster's article on class names leans more on the "wise fool" reading. The honest summary is that the argument-word came first and the joke helped fix its shape.
A 1688 book, Randle Holme's An Academy of Armory, shows the forms in flux. It ranks students as "Fresh Men," then "Sophy Moores," then "Junior Soph, or Sophester."
Britain eventually dropped the system in favor of first year, second year and final year. North American colleges kept sophomore, alongside freshman, junior and senior. The adjective sophomoric, "immature and overconfident," keeps the folk meaning alive.
The mōros half has its own descendants. It gave English moron, a term coined in 1910 as a clinical label that soon became an insult. It is also inside oxymoron, "sharp-dull."