Why is the opposite of "greater than" "less than"?
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.
As you might suspect, the symbols (and thus their names) come to us from the world of mathematics. According to Wikipedia:
The symbols < and > first appear in Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas (‘The Analytical Arts Applied to Solving Algebraic Equations’)...
So, in the world of math, as I understand it, less is not the same as smaller.
But then, why greater instead of more? According to this page:
The 3 Rules for MORE/GREATER/LESS/FEWER than…
If COUNTABLE (dogs, apartments, opportunities, agencies, people)
-> then Use MORE/FEWER than combinationIf COUNTABLE, but related to time, distance, or money OR if NOT-COUNTABLE
-> then Use MORE/LESS than combinationFor BOTH COUNTABLE & NOT-COUNTABLE, if there is a comparison made between the LEVEL or DEGREE or NUMBER of something
-> then Use GREATER THAN/LESS THAN combination
So, because there is a comparison going on, we use greater than/less than. (Note that that site includes no references, but if you want something more definitive, I'm sure that the Google can help out.)