Funny you say this, I used to live in Eastern Canada. Fans of many teams out there, but mainly Leafs and Habs. Anyway, back in the late 90's and early 2000's when the Leafs were playing the Sens every year in the playoffs, as much as I was cheering for the Leafs the Sens were my 2nd favourite team. Keep in mind, there was no local (Toronto or Ottawa) media bites online or anywhere really at that time (not for me anyway).
It was not until I moved to Ottawa and started talking to locals, listening to local sports radio etc that I learned of this incredulous hate for the Leafs and more so the city to Toronto. I found it beyond weird, but the depth of the despise turned me against the Senators pretty quickly. Like you, once I joined this site it became clear this was a Canada wide thing. The inferiourity complex people have with the city of Toronto is outright comical, petty and quite honestly weird.
I get that people who live in NHL cities have a certain pride that that team represents their city, but I can also tell you that those who do not live in an NHL city and support a team from that NHL city, almost never have any association to the city itself... just happens that the team they cheer for plays in that city.
Anyway, I guess the TL;DR is, I cannot cheer for any Canadian team. I wish I could, but I guess I too am petty.
PS - The last time I remember cheering for a Canadian team was the '06 Cup finals; that was a great run by the Oilers!