During the American revolution, the 13 colonies asked Canada, particularly Quebec to join the war against England. They declined. The primary reason was the passage of the Quebec Act of 1774: a series of promises to preserve French language, culture, and Catholicism in Canada. As a consequence, the clergy encouraged loyalty to the crown.
Prior to that time, Canada was too dependent on England (Canada does not have a year round warm water port like say, New York) and after that time the UK provided commonwealth status benefits combined with a weaker grip.
A more profound question might be why did America call for independence. Hint: England expected the colonies to pay for some part of the French-Indian war and abide by English embargoes that, if ignored, would make them rich.
We can all agree, however, that it's a good thing America decided to throw off British oppression, if not, we'd all be speaking English today. Is that what you want? Huh?!
Source: Canada and the American Revolution by Gustave Lanctot.
hi! You'll find some more information on this in the FAQ (link on sidebar)
Some Canadians did call for independence. There were even 2 armed rebellions for independence in 1837- one in English Canada and the other in French Canada. But the revolts failed, and most Canadians were 'conservative' in the sense the preferred to keep the status quo- British rule.
In Quebec the local French-speaking elite- the clergy and seigneurs- were co-opted by the British rulers who allowed them to maintain their language, culture and Catholic religion. So the Francophone elite in Quebec supported British rule and the general Francophone population mostly followed the lead of their clergy and seigneurs, with the exception of some radicals.
As for English-speaking Canadians, most of them arrived after the American War of Independence. They were Loyalist Americans who supported Britain against the patriots who wanted independence from Britain. So when they moved to Canada, they naturally continued to support British rule.
Another factor was the War of 1812, where Americans invaded Canada, and burned and looted the capital York (Toronto). This war may have led to lasting anti-American feelings, especially in Ontario, the most populous English-speaking Canadian province. This meant Canadians were determined to avoid coming under American rule, and allegiance to Britain set them apart from the USA.
Like I said before, there were some Canadians who wanted independence and were even willing to take up arms to get it. But they just failed to win enough popular support to succeed because the general population preferred the status quo (British rule).