You might be interested in the top comment on this thread, which features a collection of previous responses addressing Canada and the American Revolution, curated by /u/OldWorldGlory. To summarize: Canada was recently conquered by the British, a recent influx of British immigrants meant there was stronger loyalty to the Crown, and divisions between the original French Catholic settlers and the Protestant Americans didn't help to engender feelings of brotherhood.

Furthermore, if we look at other British colonial possessions at this time, India was still administered largely by the British East India Company, and not directly under the control of the British government. The First Fleet didn't arrive in Botany Bay until 1788, several years after the conclusion of hostilities in the Revolution. The situation simply wasn't comparable in many other colonies to that in the American Colonies, which had enjoyed a remarkable level of independence and preferential treatment within the Empire.

There are a variety of historiographical explanations to answer this very question that go well beyond vague explanations like "taxation" and "loyalty."

Looking north to the British possessions that would become Canada (at the time there were three colonies: Nova Scotia, Quebec, and Newfoundland), it is important to recognize that their British origins were much more recent. The British had only fully conquered Nova Scotia and Quebec after the mid-eighteenth century and these colonial governments were more closely associated with the British metropole. As Elizabeth Mancke points out, unlike the 13 American colonies, these 18th Century British colonies were founded after the Glorious Revolution of 1688 and therefore recognized the concept of Crown-in-Parliament. Earlier British colonies, like Massachusetts for example, swore their allegiance to the Crown alone and there is good deal of scholarship that recognizes the origins of the American Revolution as a revolt against Parliament that later encompassed the Crown when King George III did not aid the colonies. In reading the Declaration of Independence, Benedict Anderson notes, "Eighteen of its twenty-three paragraphs (one of these has nine subparagraphs each beginning with 'For') commence accusingly with the word 'He'." By 1776, the enemy of the 13 American colonies was King George III. In colonies like Nova Scotia, however, Parliament, in the King's name, appointed royal governors to keep control centered at the capital of Halifax, rather than let local democratic town governments develop as was the case in New England. Furthermore, the establishment of the Admiralty Court at Halifax to enforce British trade laws in North America shifted a good deal of the British Navy north bringing investment and employment to what was an otherwise struggling colony. The presence of the British Navy also meant that rebellion was much less likely.

When it comes to French allegiance (or more accurately: defensive neutrality) Quebecois colonists recognized that the Quebec Act of 1774 allowed not only the freedom to practice their Catholic religion, but also a fairly autonomous local government that allowed colonists to continue their lives largely undisturbed. The Quebecois had been suspicious of the far less tolerant American colonies, especially the New England colonies where even in the religiously tolerant colony of Rhode Island, Catholics were banned from open practice and political participation until the mid-nineteenth century.

Rather than use vague terms like "loyalty" to argue why British colonists (and their French counterparts) in Canada remained within the British Empire, it is important to note that the British government intentionally established the colonial governments in newly conquered territories to avoid the type of independent democratic thought that had been growing in the American colonies for the past century.

Secondly, it is equally important to shift attention to the British Caribbean. Like the 13 American Colonies, the British had established island colonies in Jamaica and Barbados well before the Glorious Revolution and so, in theory at least, these colonies shared more in common with the 13 mainland colonies than with the recently conquered regions of Canada. However, the demographic makeup of these colonies was incredibly different from all the American colonies with the exception of South Carolina. In the British Caribbean, sugar plantations dominated the economy. Unlike on the mainland, the majority of these Caribbean plantations were large-scale operations employing dozens and even hundreds of enslaved Africans. Unlike the mainland, which developed a self-reproducing slave population, the Caribbean islands relied heavily on continuing shipments of African slaves from Africa and other regions of the New World. These plantations were also run by "absentee planters." These absentee planters owned the plantations, however, rather than live on and manage their plantations directly, these owners chose to reside in the British Isles and appoint overseers to mange the operation. Despite a move toward manufacturing that would culminate in the 1830s, these sugar plantations were still highly valuable in the late-eighteenth century. While British taxation strategies may have been unpopular on the mainland, they served to benefit Caribbean plantations. Furthermore, the absentee planters made up a good portion of the British Parliament that voted to enact such taxes. When the American Revolution began, absentee planters were certain to protect their wealth in the Caribbean and the British Navy quickly moved to prevent American, French, or Spanish attacks on these islands. White colonists on the islands feared the Revolution would inspire slave rebellions throughout the Caribbean and threw their full support behind the British rather than support a dangerous republican cause.

Following American victory, many historians note a shift in the British Empire away from an Atlantic Empire and towards the Indian Ocean. However, this "Second British Empire" was largely influenced by British subjects who had direct experience in North America and the Caribbean during the American Revolution. The wave of Loyalist emigrants brought with them what one historian has dubbed "The Spirit of 1783," equally as transformative to the British Empire as "The Spirit of 1776" was to the American Empire.

Sources:

Maya Jasanoff, Liberty's Exiles

Elizabeth Mancke, Fault Lines of Empire

Andrew J. O'Shaughnessy, An Empire Divided

Benedict Anderson, "To What Can Late Eighteenth-Century French, British, and American Anxieties Be Compared? Comment on Three Papers." AHR (October 2001)

Ann Gorman Condon, The Loyalist Dream for New Brunswick

For the record there were protests against taxation in the West Indies after the Seven Years War, although these did not ultimately lead to a quest for independence.

Specifically, the proposed Stamp Tax in 1765 spurred several riots in the Leeward Islands. In Basseterre in St. Kitts, a crowd of some three or four hundred surrounded the house of stamp distributor William Tuckett, roughly handling him until he escaped from town; afterward they followed him to Nevis to prevent him issuing stamps, burning two houses in the process. There were also disturbances in Antigua, while Jamaica and Barbados were more acquiescent toward the new tax.

The protests were largely spurred by fears of the loss of trade from the mainland North American colonies, although the burden of taxation fell more heavily on the West Indies than in North America - the single greatest consignment of stamps in British America went to Jamaica, even though its white population was considerably smaller than most mainland colonies. And some members of the local elites opposed the new taxes as a matter of principle. (Note that in 1651-2, Barbados had entered into an agreement with England that established the principle that "no taxes, customs, imports or excise shall be laid, nor levy made on any of the inhabitants of this island without their consent in a General Assembly" - a point of view that was reprised by the mainland colonies in the 1760s.)

But the Caribbean colonies did not join in the protests against the Townshend Duties that were introduced in 1767, largely because West India lobbyists managed to secure exemptions for the islands from the new customs commissions and vice-admiralty courts established under the new legislation. There was therefore little reason for them to protest, since the duties had little effect on their trade.

It was not until the passage of the Coercive (or Intolerable) Acts of 1774 that West Indian colonies once again became involved in imperial controversies, as the legislatures of several islands drafted resolutions to support Boston and implore Parliament to reach an amicable solution with the mainland colonies. One of the most remarkable of these resolutions came from the Jamaican assembly, expressing concern about "a plan almost carried into execution, for enslaving the colonies, founded, as we conceive, on a claim of parliament to bind the colonists in all cases whatsoever," while asserting that the "most essential rights of the colonists have been invaded, and their property given and granted to Your Majesty, by men not entitled to such a power."

But while this logic was enough to spur the assembly to support the mainland colonies, it certainly was not grounds for them to join in the rebellion against the mother country. (And the fact that the Caribbean colonies depended heavily on the British military for their defence had a lot to do with this.)

Sources: Andrew J. O'Shaughnessy, "The Stamp Act Crisis in the British Caribbean," William and Mary Quarterly, 51 (1994), 203-226; Matthew Mulcahy, Hubs of Empire: The Southeastern Lowcountry and British Caribbean (2014).