The fact that you can only stay in the United States for 6 months and then are required to leave again has nothing to do with Canadian citizenship. That is simply United States policy regarding foreign vistors. That limit is only imposed if you don't have a visa which allows you to stay longer. Provided you have a visa, you're able to stay until your visa expires.
Canada has a similar policy regarding visitors with American citizenship. Americans are able to visit Canada for up to 6 months without needing a visitors visa. If they want to stay longer than six months than they have to go through the process of applying for a visitors visa (or a student visa, or even a work visa).