I keep on seeing arguments for and against Rommel's brilliance. I'm currently reading "How Hitler could have won WWII" by Bevin Alexander and he keeps talking about how Rommel kept overrunning the Brits and even destroying significant forces while at it. He also states that Rommel had very little logistical support from home and about half of his units where underequiped Italian divisions. He knew to focus his forces at a decisive point while the Brits spread their tanks out. All this points towards next level tactical acumen. He was basically continuously routing a superior enemy. I'd really like to know why some people consider him overrated.
Short answer: Rommel was a skillful commander, with demonstrated accomplishments at the tactical, operational and strategic levels; but "was X a brilliant general" and subjects like "How Hitler could have won WW II" are pop history, more entertainment for the casual reader than useful historical insight. What a historian can tell you is that the question addresses only a thin sliver of "what happened and why?", and to understand World War II, or even the North African campaign you need to think about a lot more than genius.
Discussion:
Rommel has a career demonstrating his considerable capabilities and ingenuity in many situations. He had a distinguished record in World War I as a small unit commander, demonstrating skill and initiative in tactical operations. In the interwar years, he wrote an influential military science text Infanterie Greift An (= "Infantry Attacks"). In the Second World War, he demonstrated skill at the operational level, and to the extent that he had input, at the strategic level. So he was one of Germany's most capable military leaders; but in war the public has an appetite for heros, and there's reason to think that there's a little more nuance to Rommel than just the myth of "The Desert Fox":
The German commander-in-chief in the Mediterranean, Albert Kesselring, though he claimed that Rommel was 'unsurpassed in the command of armoured units and in the conduct of raids', thought it true only so long as 'his nerves did not desert him', which they seem often to have done, judging from Kesselring's account. More important, Kesselring considered Stumme - usually ignored or belittled by Rommel's admirers- 'emotionally better balanced, equipped with more of a sense of humour than Rommel', and able to create 'tolerable relations with the Italian commanders', as well as boost German morale. Arrogantly ethnocentric, ruled by his 'fever for action', and disdainful of his Italian allies, Rommel deprived the Italians of their share of captured goods, precluded formulation of a joint strategy, and turned the chain of command in Africa upside down by constantly seeking Hitler's intercession in order to avoid having to obey his nominal Italian superiors
But . . . this isn't what academic historians _do_, for the most part. "Great commanders" has been a popular literature since antiquity, it's one of the oldest literary forms, and we even have commanders like Caesar writing such books about their own "brilliance". There's a huge market for books like "How Hitler could have won WWII" and shelves groan with worshipful biographies of various leaders and commanders but typically they're not interesting to the professional historian.
Why?
Because wars are fought by nations, by societies, and by specialized segments of these societies with a highly particular organization: armies are a kind of social machine. Fixating on the guy at the top can be entertaining popular history, but it's a relatively poor guide to "what happened". There's a legitimate place in looking at war as a kind of chess match, and arguing about the relative merits and influence of Alexander the Great, Orde Wingate and Võ Nguyên Giáp -- but it tells you only a little. If it's all you know about a conflict-- then you don't know much.
Finally, military "brilliance" is overrated. One of history's most celebrated generals, Napoleon, was plainly an extremely talented commander. For all those talents, what did it get him? Born on a small island . . . he died a prisoner on a smaller island. And the France that he ruled for the better part of two decades-- for all the war and death, the frontiers of France in 1815 were little different from 1797, and they'd lost their overseas empire.
So if you look at "what historians think" -- they don't really much concern themselves with "X is over[under] rated". Even when it comes to military history, command matters less than you likely think it does. As Napoleon put it: "God is on the side of the big battalions"-- the nation that wins is far more often the side with the larger army, the better technology, the most factories. Being average, well equipped, numerous and persistent is usually good enough. Was Montgomery "more of a genius" than Rommel? Does it matter? Montgomery's army and the machine behind it was more capable than Rommel's, whatever the relative merits of these two commanders may have been.
So you may know Napoleon's name-- but do you know the name of the guy who organized his conscription policy? (Lazare Carnot, "the Organizer of the Victory"). At the end of the day, a lot of Napoleon's "genius" was a steady supply of warm bodies . . . which the Emperor with all his skill delivered to the grave.
Sources:
On Rommel
Of Myths and Men: Rommel and the Italians in North Africa, 1940-1942
ERWIN ROMMEL : LE HÉROS DE LA PROPAGANDE
Central Mediterranean Sea Control and the North African Campaigns, 1940-1942
German Military Incompetence Through Italian Eyes
On the importance of things other than military genius to success in war
Supplying War: Logistics from Wallenstein to Patton
Robespierre, Danton, and the Levée en masse
MAJOR LOGISTICS LESSONS OF WORLD WAR II
The Economics of World War II: Six Great Powers in International Comparison
The Wages of Destruction: The Making and the Breaking of the Nazi Economy
. . . and if you can read only one book to get a different perspective on "how war works, as seen by a historian" -- read The Strange Defeat by Marc Bloch, he was a great historian, a French soldier and a Resistance leader,