That Hollywood whitewash of a movie A Bridge to Far carefully doesn't examine that fact and sadly that movie seems to be be the main reference source for so many
How to take a bridge? General Gavin of the 82nd Airborne himself said "both ends at once" , sort of duh! Airborne Troops can be dropped over natural obstacles like rivers, duh again. So airborne troops placed on both sides of a bridge by parachute or glider is the standard method of attack. Gavin DID this method for the attack on the Graves Bridge by the 504th.
Yet Gavin did nothing like this for Nijmegn, all his troops were dropped on the south side of the Waal river. From the very start HIS plan had no means to take the Nijmegen bridge other than by frontal assualt. He packed a bulldozer for his trip but no boats, so the option of a river crossing was non existent either till XXX Corp came along.
I have not seen any reasonable explanation for the failure of the 82nd Airborne NOT to have captured the Nijmegen bridge on the first day (<--- core question ) . German resistence was minimal at the time of the Landing, The 82nd Division's own GS-2 reported "landed against almost no opposition". The 504th Regiment had the Graves Bridge captured in under a few hours, the 505th losses for the entire first day was 63 men killed, wounded or injured (out of 3000 men).
The 504th had taken their bridge successfully, the 505th task, was to clear the Groesbeek 's Heights and send patrols into the Reichswald ( Gavin's obsession). The 508th tasks were to block the road at Mook and then move on the Bridges at Hatert and Honinghutje and THEN the main bridge at Nijmegn.
I stress again, the only option his plan had was a frontal assualt, unless speed and surprised was used quickly upon landing. Speed and surprise were non existent either.
On Day One, the 1st Battalion of the 508th Regiment was tasked with the capture of the road bridge. Here confusion starts to creep in, Gavin said afterwards they were to attack immediately, the Regimental Commander , Colonel Lindquist said the battalion was not to attack till all other Regimental objectives were attained.
The battalion commander Lt Colonel Warren said his objective was the to prepare a defensive position near De Ploeg and then move onto the bridge itself. It was not till 1830hrs he sent a patrol forward, a single platoon and a radio section. The Dutch had reported there were only 19 Germans guarding the Bridge.
At 2000 hrs Warren moved two rifle companies to take the bridge, A & B,. B Company got lost, so only A Company moved forward. They moved slowly and at around 2200 hours, came under fire from elements of the 9th SS Panzer Divison Reconnaissance Battalion who had just arrived. From that point on, the 82nd Airborne did not have the capability to take the Bridge unaided. They had failed.
That delay is not speed and surprise by any means and is the major reason why Market Garden timetable fell apart.
One of the myths the US puts out about Market Garden is how XXX Corp was "late".
XXX Corp said they would be at Arnhem in 48 hours (2 days). XXX Corp left their start line at 1400 hours on the 17th, they linked up with the 82nd Airborne at 0830 hours on the 19th. They were still six hours in hand and 8 miles from Arnhem. They were on time at that point. The myth is deliberate to shift blame, it reoccurs constantly.
Here is where the Arnhem plan collasped, it took 36 hours of hard fighting to take the bridge, that should have been taken on Day 1.
The fault here lies with Gavin and his plan. He did not plan an attack from both ends at once. he did not have the means to do so once he landed. His plan meant his only option was a frontal assault. He only said after the event the bridge was a priority, yet his commanders below him said otherwise. He later attacked Horrocks of XXX Corp for being to slow to bring up boats when he had brought none himself.
His behaviour post battle was one of self justification. He believed he had to take the Graves Bridge and the high ground (the Grosebeek Ridge) as his priority. Those was not his orders, his orders from US General Brereton were to take the bridges with "thunderclap surprise". He didn't.
To make matters worse Gavin obsessed over the Grosebeek Heights and the Reichwald, that zone became his Divison's objective and not the Bridges. A clear case of forgetting what he was there for. He claimed at one point 1000 tanks could be in the Reichwald, the Dutch said "no" and his own patrols said "no", (a patrol of the 505th Regiment on the 18th reported no German armour). In his memoirs he blames the British for his preoccupation there. He manages to blame everyone else but himself.
Lt Colonel David Frost of the 2nd Parachute Battalion at Arnhem Bridge said post war
The worst mistake of the Arnhem plan was the failure to give priority to capturing the Nijmegn bridge. The capture would have been a walkover on D-Day, yet the 82nd Divison could only spare one Battalion as they must at all costs secure the Groesbeek Heights where the Corps HQ was to be sited"
The most distasteful thing to come post war, is the myth put out by the Americans that the British XXX Corp stopped after capturing the bridge and its their fault for that the operation failed. Not the fact the 82nd Airborne failed and caused the delay itself. XXX Corp had to reassemble, rearm, resupply after very heavy fighting before moving on again, only 5 tanks were across the Bridge, (commanded by Captain Lord Carrington, a senior Govt Minister under Thatcher later in life.) His version of events over the bridge differ markedly to the American events, so it comes down to who had the best reason to try and pass the blame? Who spreads inaccurate myths on other aspects?
A post script- The 3rd Battalion 504th Regiment river assault is rightly described as brillant. In the British XXX Corp boats, as they had none of their own, that fact clearly shows Gavin's initial plan was a failure. Its only fair to remember though that with them went the British 615 Field Squadron and 11th Field Company of the Royal Engineers. They have been whitewashed out of history to sadly. Further during the actual crossing , the Grenadier Guards Tanks along with the US 505th Regiment were attacking the south end of the bridge, so the assault whilst highly dangerous was not done in isolation.