The word from which it derives is actually wholely English and the explanation of "wise fool" from the Greek came later. It's also not because they "sometimes think rationally." A "wise fool" is a common way to describe someone who fancies themself wiser than they are as a second year feeling confident after completing their first year would. Do you actually do any real research?
However, while this popular etymology has no doubt influenced the usage and spelling of the word, it seems originally to have been a wholly English formation, based on 16th-century variants of the word sophism; in the spelling sophumer it is recorded in OED from 1653. The word originated at the University of Cambridge, where it is now obsolete, but by 1726 it had crossed the pond to Cambridge, Massachusetts, when it was used at Harvard, and to Yale by 1764 (where the spelling sophimore was originally preferred). The word sophomore has begotten an adjective, sophomoric, and is also used attributively to mean ‘second’ as when an author’s second novel is called his or her “sophomore effort”.