My dear British friend. That wasn't really a question was it now? It was more of a dressing down as you Brits would say--some well deserved, some quite off the mark.
THe outcome of a war, like a fistfight, is not necessarily detrmined by who wins the most rounds, but rather who is laying on the canvas at the end of the contest and who is still standing. In light of General Cornwallis' decisive defeat and surrender at Yorktown, King George and Parliament simply decided it was not worth the farthing to sink further manpower and resources into a colonial war, which is why the only British flags flying in these of your former colonies are flying over your embassies these days.
You are quite right about us not winning that one by ourselves of course. An largely agarian collection of rebellious colonies with a population of three or four million could not possibly have defeated a nation of over forty million at the time possessing of the largest and best navy in the world. French supplies for our war effort played a great role, and the French naval interdiction of relief and evacuation for Cornwallis was critical to that knock-out blow at Yorktown.
Even with that victory, Britain certainly could have fought on, and possibly won, but the question was, at what cost? Here was a sparsely populated group of colonies, not really producing an enormous about of export trade or tax revenue that was requiring enormous resources to occupy in light of its rebellious state. Britain had other more pressing interests, including the French and the Spanish, and a vast empire aside from us with which to concern itself. We never really had to "win." All we had to do was become a sufficient thorn to make you want to be rid of us--and that we accomplished--with some help as you point out.
As to the War of 1812, you did beat us about the head and shoulders for a good bit of it yes. Bigger army, bigger navy, not surprising. But my friend, your recollection of the Battle of New Orleans is quite faulty. It was, in fact, one of Britain's most embarrassing and costly defeats in a land battle of the era.
Now as to not winning a war by ourselves, that's neither entirely accurate, nor very charitably expressed. I think it is fair to say we won the Spanish-American War by ourselves. The major conflicts in the 20th century, the two World Wars, were not really our affair at the outset. Those were largely your doing, stemming from your conflicts with Germany, and my reading of the history is that in both instances you were begging for our help, and help we did.
No, we didn't win either of those ourselves, but there is little question that you would have lost each of them without us. We provided the supplies, the manufacturing base and the manpower that you simply did not have in sufficient quantity to win.
Also, in the Second World War, we largely did defeat Japan on our own. You Brits provided a little help, as did Australia, but mostly your navy in the Pacific had been destroyed early in the war and your garrisons in your colonial holdings at Singapore, Hong Kong and the like, were sitting in Japanese prison camps as we were fighting our way back across the Pacific. All the while we were fighting with you in Europe and North Africa, we were also prosecuting a war with Japan wth very little assistance from anyone. Some leand bases in Australia and New Zealand, and some troop assistance in the fight for New Guinea, but let's be fair here--we carried the bulk of the fight, the cast majority of the losses, and as I said earlier, your remarks were just not very charitable.
At the end of the day, however, I should much rather describe us as the closest of allies, not antagonists or critics of one another. However costly and possibly ill-conceived our war in Iraq has been, you have backed our play, and we are grateful in the extreme. When Argentina sought to take your Falkland Islands from you, we also provided critical support to your efforts, refueling bombers en route and and providing critical satellite reconnaisance to keep your fleet safe--very much in violation of our defensive agreements with Argentina.
We know who our friends are when the chips are down, and we are in your debt for being there when we have needed you. I only hope that you may feel the same about us.