Those are mostly semantic and completely immaterial arguments.

1: She is a foreign Queen. She lives in the United Kingdom. She is the heir to a British monarchy that was put in place by the British. On paper all things might have an equitable wording, but in practice she isn't Canadian.

2: Again this is a semantic distinction. The United States used to be the Thirteen Colonies of British North America. Sure, on paper we are a nation that came about in 1788 with the constitution and therefore have never technically been British subjects, but in practice we are the heirs to the Confederated government, which was in turn heirs to the Thirteen Colonies. In the same way, Canada was British North America. Sure, Canada itself might have on paper never been a part of the British Empire, but it is the direct heir to British North America. When Canada was born, it had the grand majority of the same people that British North America had the year before. 

3: But that's it, isn't it? You achieved democracy democratically, go with that! The United States didn't ignore its British heritage, it's still very much there, in our legal system and our economic system. You don't need to hold onto a foreign monarchy to retain your British heritage. 

Of course it's all symbolic, but we go back to point one: there isn't any need to get offended of the government decides to renounce an irrelevant monarchical tie and instead decide to be wholly Canadian.