White Canadians tend to have a negative identity based around not being American. Americans can be prideful and gloat about superiority over every country. That probably produces the rivalry you see.
However, that's for a certain type of people. American leftists tend to admire Canada for being more leftist than America. As an Anglophile, I adore Canada as a fellow settler country of British origin.
I hope that clarifies some things.
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