As a Canadian, I've always heard that during the War of 1812 it was the beginning of an identity that forged among Upper and Lower Canadians because of the various Brits, Natives, Scots, Frenchies, and Blacks that fought together against the Americans. Later I would learn that this isn't really true, but I never was able to know specifically why in detail.
What I'm essentially asking is how did this myth start, and what are some incidents from the War of 1812 that debunk this myth?
It is hard to go beyond conjecture when answering this question, because the concept of a uniquely Canadian identity is anecdotal. It means something completely different to every one. Since it is not possible to go back in time and deduce what the prevailing sentiments were in each community in British North America in the 19th century, we just can't make any definitive statements.
But if I was to start anywhere, I would say that the Upper and Lower Canada Rebellions of the 1830's, annexationist movements throughout the 19th century, and shaky French-English-Aboriginal tensions since then, would all be indicative that the War of 1812 didn't exactly create a sense of cohesiveness in Canada.