One possible reason that mathematics might have come to use greater than and less than as opposed to (say) larger than and smaller than might be that they were more natural translations from Latin.
Mathematics was largely done in Latin until the 17th century. The Latin terms were majorem quam and minorem quam, as can be seen by the first definition of the > and < signs in Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas by Thomas Harriot (see Wikipedia):
"Signum majoritatis ut a > b significet a majorem quam b" and "Signum minoritatis ut a < b significet a minorem quam b."
Major is the comparative form of magnus, which I assume was generally translated as great, since its range of meanings is much broader than large. (E.g., Charlemagne was called Carolus Magnus, or Charles the Great. Charles the Large wouldn't have meant the same thing at all.) Thus, major would naturally be translated as greater.
Minor is the comparative form of parvus, which again has a much broader meaning than small (small, cheap, ignorable, unimportant).
The natural opposite of greater in English that is compatible with this broader meaning would be less or lesser.