The basic reason for this is the fact that the people of Quebec have a different national heritage from the rest of Canada. The rest of Canada is Anglophone and was originally made up of colonies of England. Quebec, by contrast, is Francophone and was a colony of France until England won it in 1763.
Separatists feel that they are a distinct nation. They feel that their French heritage sets them apart from the rest of Canada. They feel that being part of Canada is endangering this heritage. Furthermore, they feel that Anglophone Canada has run the country in ways that help itself and hurt Quebec. Because of this, they feel that they need to be a separate country so as to preserve their heritage and to have a government that pays attention to their intersts.