The problem in general
Most educated people, when they hear the word “multiculturalism”, assume it to be synonymous with diversity. It's not surprising, since the word seems to be a conjunction of “multi” (many) and “cultural” (cultures). So the logical conclusion is that multiculturalism is simply a doctrine that says mixing lots of cultures together is good. However, “multiculturalism” is not the same as cultural diversity.
In political theory multiculturalism refers to an approach that states adopt in order to negotiate the relationship between specific cultures and other members of society. Multicultural policies are an attempt to build a bridge between the state and minority communities by looking to particular community organizations and leaders to act as intermediaries. Multicultural policies accept that society is diverse but implicitly assume that such diversity ends at the edges of minority communities. In other words, they institutionalize diversity by putting people into ethnic and cultural boxes and defining their needs and rights accordingly.
Multicultural policies tend to reinforce the differences between groups based on ethnic and religious identities. They grant certain “group rights,” often to the detriment of individual rights. They favor tradition over modernism, and community over fundamental human rights by supporting and emboldening traditional religious leaders.
In a sense, multiculturalism is a rejection of modern Enlightenment values. It's rooted in the belief that universal citizenship, equality before the law, and equality of opportunity are insufficient and that the state must actively work to protect the cultures and beliefs of immigrant communities by granting privileges on the basis of membership in these religious or ethnic groups.
As an ideology, multiculturalism encompasses a variety of approaches, not all of them inconsistent with Enlightenment, liberalism or modernity. However, it does tend to place greater emphasis on diversity than on equal rights and equal opportunities for all. Its advocates often push for value pluralism and moral relativism: the idea that different moral outlooks (both those that respect individual liberty, and theocratic or fundamentalist ideologies that do not) are equally legitimate.
Cultures, however, are not homogeneous but complex. Multiculturalism attempts to describe loose groupings of individuals with similar backgrounds, religions or language as a “culture” and then assumes that the diverse individuals within that culture belong to the same “community”. Far from protecting, say, “all Jews” or “all Muslims” from generalizations, it reinforces the political fiction of cultural or religious unity.
Rather than appeal to Muslims and other minorities as citizens, multiculturalism assumes that minorities’ true loyalty is to their faith or ethnic community. In effect, governments that adopt multicultural policies are subcontracting their political responsibilities out to minority leaders, who rarely represent their entire community and are usually on the more conservative end of the spectrum. This can lead to absurd situation like when Ontario was considering allowing Muslim faith-based tribunals i.e. Sharia law, in its justice system.
The problem in regards to Quebec
In English Canada, multiculturalism remains a sacred cow. The term is often used in contrast to intolerance or even racism, as if anyone who criticizes it must be a xenophobe who hates immigrants. But in reality, multiculturalism is itself a close cousin of racism – Djemila Benhabib calls it “multiracism” – because it exaggerates the importance of the community into which one is born, to the detriment of one’s individuality.
Multicultural policies essentially encourage immigrant communities to hold on to the culture of the country they left. This can lead to insular and ghettoized communities. Canada has been more immune to the negative effects of multiculturalism than many other countries mainly because it shares a language and culture with the global hegemon. Canadian multiculturalism depends on the dominance of American culture on this continent to keep its multicultural "mosaic" together.
This is simply not true for us in Quebec. In fact, the opposite is true. Our existence is in resistance to the dominant culture on this continent. So Canada's multicultural polices, which ostensibly work so well in English Canada, are not at all suited to our reality in Quebec, but they are imposed on us anyways.
Canada has never been a very well defined country. In fact, there have always been widely divergent interpretations of what Confederation, the so-called founding of this country, was really about. To George-Étienne Cartier, the Attorney General for Canada East during the negotiations on Confederation and the principal leader of French Canada, it represented a pact between two nations. This is clear from what he wrote in La Minerve on July 1, 1867:
"Such is […] the significance that we must attach to this constitution, which recognizes the French-Canadian nationality. As a distinct, separate nationality, we form a State within the State with the full use of our rights and the formal recognition of our national independence."
Others saw Confederation as a pact between the provinces. After all, it's the British owned provinces of North America (with certain exceptions) that got together to create the federal government. However, when the Anti-Confederation League in Nova Scotia won 36 out of 38 seats in the provincial legislature, and 18 of 19 seats federally, not long after Confederation, they found that there was, in fact, no way out after Britain refused their secession. Canada's imperial nature became evident to them at that moment.
John A. Macdonald, on the other hand, was in favor of legislative union, i.e. a unitary state with a single Parliament for all of Canada. He didn't get that but to a large extent, Macdonald achieved the type of centralized federalism that he desired. The powers of disallowance and reservation in Canadian federalism made that perfectly clear.
Nonetheless, in the early days of Confederation, there seem to have been some acceptance of the binational nature of Canada, as seen in the Manitoba Act. But that acceptance was soon thrown out the window as the demographics of this country changed and Canada basically became British Canada which begrudgingly tolerated French in Quebec since it was still the majority language there.
In the 1960s, francophones in Quebec began to reject their second class status and wanted to become "master in their own house." There was also a growing demand for the recognition of the binational and bicultural character of Canada and this was even followed up with the threat of "equality or independence." Canada responded by setting up the Royal Commission on bilingualism and biculturalism, presided by André Laurendeau, editor of Le Devoir, and Davidson Dunton, president of Carleton University.
This commission agreed that Canada should formally recognize its binational nature. But instead, Canada adopted a policy of multiculturalism. It must be emphasized that this policy of multiculturalism was adopted in 1971 under Pierre Elliott Trudeau’s government as an answer to the prescriptions contained in the commission's report, and that Trudeau's sudden rise to power at that time was largely due to his staunch opposition to Quebec nationalism.
One of his goals in adopting this policy was undeniably to drown Quebec nationalism in a sea of multiple cultures, thus replacing “bi” with “multi.” So while multiculturalism was enshrined in Trudeau's 1982 constitution, no mention is made of the existence of a Quebec nation. Canada is described as a single, bilingual, and multicultural nation. By recognizing a multitude of cultures, multiculturalism negates any notion of duality and nullifies Quebec's claim to distinctiveness on the basis of culture.
So, we have gone from being one of the founding nations of Canada (at least, that's how we saw it) to an ethnic minority similar to groups of recent immigrants. It's not that we believe that we are more "special" than Italian or Ukrainian Canadians. But let's be honest, Italian or Ukrainian culture is not being created in Canada. They are living and evolving cultures in Italy and the Ukraine, not in Canada. Immigrant communities are simply holding on to the culture of the old country and trying to pass it down to the next generation like some kind of family heirloom. Multiculturalism encourages this behavior but despite these efforts, each generation usually becomes increasingly assimilated into the dominant culture of the host country.
We are no more French immigrants to Canada than Brazilians are Portuguese immigrants to Brazil. Our culture is a 400 year old French-speaking, North American culture that has always been diverse in its own way. It (or remnants of it) can be found all over this continent. Today, however, it is only in Quebec that it is a living culture that can evolve and integrate newcomers. We were our own distinct nation long before Confederation. We are not just another ethnic tile in English Canada's multicultural "mosaic." Canadian multiculturalism without any constitutional recognition of Quebec's distinctiveness is an inherently assimilationist policy, and it is for this reason that it is widely rejected in Quebec.