Well, in a defensive war the defender need merely survive to win. (Sun Tzu or Klauswitz, possibly.)
That's the thing...the British were fighting the war defensively until 1814 (with the Americans invading British territory in Canada), when Napoleon was exiled to Elba. Once Napoleon was gone, they wanted to end it decisively, and they turned more aggressive; but the War of 1812 was never about the reconquest of America for the British.
The war started because the Brits were supporting indian tribes that stood in the way of westward expansion, blocking trade in the Atlantic and impressing American sailors into the British Navy. The British weren't itching to invade though, and their support of the natives was not clearly aimed at screwing with us...to some extent it was just making nice because the British didn't want wars with the natives in Canada and wanted to keep them as allies in case an American invasion of Canada was ever launched.
And...guess what...America took the opportunity to try to seize some of Canada. While it seems unlikely that permanent annexation of Canada was a war goal, America was decidedly expansionistic and it's unclear our complaints about arming the natives were really very strong (except that they were arming people living on land we wanted to eventually settle, and that was ipso facto bad for us).
It's not entirely cut and died that we were merely "defending" ourselves and the British solely the "aggressors." We had good cause to declare war, imo, but it was a complicated situation.
In the end the war settled little. The trade blockades ended because the British war with the French ended. Impressment ended for the same reason. The War of 1812 had nothing to do with those, and those were the most direct claims we had for war.
What America did win was a promise from the British to stop trading arms with natives in Michigan and northern Ohio, which ended any hope the natives had of defending their claims on that land.
