A little history about the role and name of the sergeant.
Sergeants were originally, during the middle ages, professional soldiers who fought as knights but held no noble title. That is: In armour, mostly on horseback and in formation. They were mostly mercenaries who filled up the nobles' ranks in combat and trained the forces held by the nobility.
This is where the NCO's role as an instructor comes from. In a time when the only professional soldiers were mercenaries or nobles, there was little time to train the rallied forces or militia. The sergeants took it upon them to train the infantry and nobility in warfare. The ancient picture of a sergeant standing behind a formation of pressed infantry -holding a lance too keep them in place comes from this time.
During the reconquista and during the crusades sergeants fought with the knights of different orders and kings. Indeed the term sergeant became a rank in some of the orders of the Holy Land.