Why does a Lieutenant General outrank a Major General?
This goes back to the origins of the ranks in the armies of England. The rank of Captain General as the most senior officer in the Army was formally established in the Restoration of the monarchy in the time of Charles II (although the term had been used previously). The first person to hold that formal rank was George Monck, 1st Duke of Albemarle, appointed in 1660. The ranks below this were Lieutenant General and then Sergeant-Major General. In time, the “Sergeant” was dropped and the title became “Major General”.