So, knight isn't really a military rank in the way we're familiar with, denoting a place in a rigid, fixed hierarchy through which men are promoted based on seniority and merit. It is a social and economic rank with military connotations. The old Duby model is that knights were common soldiers who seized power after the collapse of the Carolingian empire in the 9th century and gradually became the new aristocracy, becoming recognized as such by the 12th century. Dominique Barthélemy has argued strongly against Duby's new aristocracy and instead claims that French knighthood was a direct continuation of the old Carolingian nobility, and that by definition, all nobles were knights (regardless of whatever higher rank they held) and all knights were nobles. I lean more towards Barthélemy, but I also think that Duby was a little bit right in thinking that the status of knights rose over time.

However, with that rise in status, knighthood became more expensive and, consequently, exclusive. Between the cost of increasingly sophisticated and/or elaborate armor, weapons, clothing, horses, and the other gear, and the financial and social obligations imposed on knights, especially in England, the number of dubbed, proper knights available in western Europe dropped like a rock through the 13th and 14th centuries. Increasingly, the military role of the knight - that of armored horseman, capable of fighting afoot or on horseback - was filled by non-knighted individuals called esquires and armigers, many of whom came from knightly families but lacked the wealth to be knighted. This is not to say that knights wholly absented themselves from war - many fought as proto-officers in the Hundred Years War - just that they were no longer anything close to a majority of the men taking the field, and became less and less as time went on. It had become primarily a socio-economic designator.

The modern ranks you're referring to are almost wholly from the early modern period (Renaissance or later), and thus developed after knight had ceased to have military significance. Captain is a medieval rank; sergeant was a class of soldier, a professional who was below the knightly class. Colonels didn't emerge until the 16th century, as did generals. Bannerets (wealthy and prestigious knights who led a company of other knights), vintenars (commanders of twenty infantrymen), and centenars (commanders of one hundred infantrymen) have ceased to exist.