[Legbreaker]

Firstly, Rommel was a good Divisional commander. He was not great at commanding anything much larger.
Secondly, Market Garden, in theory, was a brilliant plan. Unfortunately the necessary intelligence was not passed back to those who needed to know about it, and that little which did get back was basically dismissed as there was little supporting evidence. Montgomery cannot be blamed for not knowing about the presence of two understrength SS Panzer Divisions in Arnhem if he hadn't been personally told about them (amongst other intel deficiencies).
Another problem with the operation was the radios used by the British Paras - they simply didn't work due to (I think) moisture getting to the crystals or something... If they had, then the dire situation could have been relayed back to HQ and the Poles dropped earlier (and on the right side of the river), supplies dropped in amongst the British soldiers instead of in fields covered by the Germans, and about a dozen other things too.

There were a number of other issues such as the bridge being blown in the face of the US 101st which held up the advance by about a day, the stubborn defence of the bridge at Nimegen, and the single narrow road up which nearly every man, tank, artillery piece, and especially supplies was to move. Yes, it was a complex plan, but if it had worked, if the British Paras had been able to hold out another day or two and armour reinforcements arrived....

And now on to the reason the British were so hesitant - they'd been fighting the war just a bit longer than the Americans - a couple of years longer.... The British manpower reserves where almost spent, they simply couldn't afford to throw men away on operations that only had a marginal chance of success unless sufficient reserves were available to at least hold the gained ground. The Americans on the other hand hadn't really fought before Italy (Africa doesn't really count as a major engagement when you consider how few Germans were actually left and how few operational tanks Rommel had available most of the time). The Americans also had a massive pool of reserve manpower they could draw upon and hadn't suffered the near catastrophe of Dunkirk, nor Rommels drive across North Africa and into Egypt.