There were rumors going around the army that if he gave the orders to evacuate, General Washington would reward any soldier who lit the fire that burnt down New York City. It would've made sense, as a good tactical maneuver... New York City was the perfect location for Howe to organize his campaign. He knew it, and Washington knew it. It was in the middle of the colonies. He could cut off aid to New England (which was the hotbed of opposition.) He could winter his army and navy there. The Americans would be unable to take the city back.
However, Washington wanted Congress to make the ultimate decision, so that if there were later complaints, it wasn't on his shoulders. And Congress said no. Washington regretted that decision but (so far as we know) he never gave the order to burn the city.
The sentiment was surely there however... and, the army felt it!
That's why the congress got voted for, I suppose -- to decide about the things that impact civilians the most. I have to say, I'm rather glad they didn't burn the city down, and I think Freddy's point about Charleston is a good one -- no use having your own people set against you, even if it is a good tactical decision!
Sometimes the man at the top just has to bite the bullet and stop hoping someone else will make the tough decisions for him. Especially in war. Leave it to the politicians to run things and you can guarantee it'll go pear-shaped!