Why does a lt. gen. outrank a maj. gen., but a maj. outranks a lt.?
Why does a lieutenant general outrank a major general while a major outranks a lieutenant?
This question has gnawed at me for years, Bob. As near as I can make out, here's the deal: In your modern army (modern defined as dating from the 1500s onward), you've got three basic units: your company, commanded by a captain; your regiment, commanded by a colonel; and your army or division, commanded by (ultimately) the sovereign. In the past as today, the individuals who actually held these lofty posts, sovereign included, were often no-talent dweebs whose principal qualification was that they had clout, noble blood, or some unsavory combination of the two. Lest the army be massacred, those behind the scenes manuevered to have "lieutenants" (deputies) appointed to assist the nominal commanders. These lieutenants, lieutenant colonels, and lieutenant generals did much of the actual decision making.
To help them with the scutwork of war, the lieutenants turned to parties known as "sergeants-major." You had a low-level sergeant major who kept the grunts in line; a regimental sergeant major who got the companies organized for battle; and a sergeant major general, who helped get the army in battle order. For simplicity, the regimental sergeant major eventually became a major and the sergeant major general became a major general. I'm oversimplifying to beat the band, you realize. But the point is, major-somethings (or something-majors) have always been outranked by lieutenant-whatevers.