That’s one of the more insidious ‘reasons’, that the 82nd was somehow to blame for M-G failing. The 82nd commander was ordered (by his superior, General Browning) specifically not to go for the Nijmegen bridge until he had taken the Groesbeek Heights, and then bridges at Grave, Malden, Heumen, Hatert, Honighutje and then and only then, the Waal bridge. Even so, the 82nd got within 400 yards of the Nijmegen before meeting impenetrable resistance on the first day.
One of their drop zones for reinforcements were overrun by the Germans, who were (surprise!) unexpectedly powerful all up and down the main highway. The 82nd quickly took the drop zone back, but only at the cost of pulling some men back from the bridge-attack forces. When XXX Corps arrived, they were unable to take the Nijmegen bridge for a day after their arrival. (Note that the 82nd was not all landed the first day - it took two more ‘lifts’ to bring it up to snuff.)
I’d say the 82nd did pretty darned well. Better than the British 1st, but that’s another story.
XXX Corps was slow, and continued to be slow, even with the Nijmegan bridge taken. Told they should be at the Rhine in three days, across the Rhine in four days they reached the vicinity of the south of the bridge in nine. The crossing at Nijmegen took less than a day once XXX arrived at the bridge. And then XXX Corps… stopped. For more than a day.
So what went wrong?
XXX Corps was presented with a hopeless task: reach and cross the Arnhem Bridge in three days. Up a highway under German artillery (and, at Eindhoven, Luftwaffe), infantry, and tank attack, requiring XXX to turn units back to clear the road.
1st Airborne was presented with a hopeless task: land 8 miles away from the objective, and walk there under heavy opposition. It’s a wonder that anyone reached the bridge, much less Frost’s brave, abandoned battalion.
82nd and 101st were presented with too many tasks, with forces not complete for three days (via the various airlifts).
It was a shambles. Declaring a 90 percent success is putting a bow on a turd. 90 percent success is still a defeat; and with Caen, Antwerp, and this, made Montgomery a well-respected (somehow) 0 for 3. Failing to take “a bridge too far”, if it’s the objective of the whole excercise, is failure of the entire operation.
What went wrong?
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underestimate of opposition. Montgomery’s plan not only required the German opposition to be light, it depended on German opposition being non-existent. Any German forces after breaking “the crust” at the front were expected to be whisked away. That the Germans might react in violent and clever ways simply did not occur to him.
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lack of aircraft - There simply weren’t enough transport aircraft to do the job. Rather than take that under advisement, Montgomery just ignored it. Transport aircraft from the “first lift” were expected to all survive that operation, and thus be able to drop reinforcements and supplies in the second and third “lifts.” Even so, the airborne elements were not expected to be completely available for three days (note this is the same amount of time expected for XXX Corps to actually reach Arnhem.) The plan also assumed (indeed, required) perfect weather in England and in Holland.
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lack of flexibility - the plan required use of one main highway to run the whole way, with no impediments by the Germans. 1st Airborne had to seize the (entire) bridge at the end of that highway, the US airborne divisions had to seize every bridge along the way, and XXX Corps had to roll up this highway at high speed. Any ‘variation’ would throw everything off. As it was, a couple of anti-tank guns would hold up all XXX Corp completely.
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lack of appreciation of the realities of the plan. That XXX Corps would scream north and take the bridge at Arnhem required that no additional supplies would be needed (supplies issued to the armored units of fuel and ammunition were for four days.) In reality, pretty much everything was in the wrong place when needed, and so… traffic jam. Huge traffic jam. Which slowed everything down.
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lack of infantry - XXX Corps had to wait north of Nijmegen for a day, waiting for infantry to come up. That is, the traffic jam made sure that the infantry needed by the armored units in the front were incapable of being there in a timely fashion.
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Groupthink - Montgomery himself. There’s a concept that encapsulates M-G; that Montgomery ignored everything that might make the operation fail. His subordinates, a number of whom were not so sure about the whole thing, were cowed into nodding their heads and saying (though not believing) that the thing would all just work. And so, off all those men went off to die.
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Fragility - Montgomery seemed to simply not be aware that any failing all along the way of the advance would ruin it. But a whole chain of unqualified successes were required.