Why pick two Generals who lost?
I should ask you a more important question: Why not?
Lee first: Lincoln was the most overrated President in our country's history, and a complete buffoon. But he made a few good decisions. One, which sticks out in my memory, is his first choice of Commander of the Army of the Potomac, Robert E. Lee. A top-tier graduate of West Point, and an ardent opponent of chattel slavery (not that that has anything to do with judging him as a general). Lee, of course, politely and honorably refused the offer, saying he could not command a force against his homeland, Virginia. (and to me, such unwavering loyalty does have quite a bit to do with judging a soldier). He commanded an inferior force against a superior foe, my country's own US Army (I am a loyal american and glad my grandparents chose to come here some 70 years ago, but give credit to the enemy when it is due. I suspect you are not doing this.) Lee's army was outmonied, outmanned, outgunned. The CSA population was maybe one-tenth of that of the USA, and the money-race was even more one-sided, yet he won battle after battle. Only after so many good sons of the Confederacy were lost that they had to choose from among small boys and old men did he start to lose. And often decisive defeats were only the results of historical accidents (private soldiers mistakes, etc.) Yet Lee managed to hold out against a superior force for four years! And, even in defeat, he was magnanimous. He negotiated a fine surrender for his officers and men, allowing them to keep their dignity and their sidearms, and return to their farms like gentlemen. Americans like Robert E. Lee make me proud to be an American.
As for Rommel, many of the comments I made about Lee can also be made about Rommel, with the addition that Rommel worked for a madman, and, somehow, he managed to keep at bay some of the best armies the world has ever assembled for years. I think that his command of the Seventh Panzer Division in France was his most impressive military conquest. His crossing of the Meuse River was a tactical triumph against steep odds. Sure, you correctly point out that his command of the Afrika Korps wasn't outstanding. And he never really faced a good opposition until the First Battle of El Alamein and Operation Torch. And his defense of Tunisia was a hard fought battle in vain. My personal opinion is that Rommel's campaign in Africa and his command of the Afrika Korp was overrated in its importance to the German Reich and his brilliance in the desert. One of the main reasons why I have such great respect for him as a commander was because, like Lee, he was such a great Patriot. If he would have fought in the Great War, he might have been able to prove himself even to your satisfaction, though somehow I doubt it. Maybe he earns my vote here not just because he was one of the best Generals of the past century, but because of the man that he was. One of my favorite WW2 people to study! Rest in Peace, Herr General.
I'd just like to add, once I noticed that Rommel wasn't among the choices, it really was hard to choose between Washington and Lee. On another day I may very well have chosen Washington, and for many of the same reasons.
