Originally Posted by EnDz0n3
Refresh my memory: Were they ever called Avengers in the movie?
Nick Fury reactivated the "Avengers Initiative" and then the Shield agents track down/offer Hulk, Captain America and Iron Man to join the Avengers Initiative. Basically those three are part of the Avengers Initiative and they are called as The Avengers for short.
You keep referencing the other movies and you still don't get it. Magneto and Mystique weren't part of the X-Men. Can you imagine if Professor X told Magneto and Mystique that they were part of the X-Men, Magneto and Mystique would probably shook their heads in disagreement because when the word "X-Men" first came up, Magneto and Mystique already left Xavier.
If you watched the movie, its a common sense that once Magneto and Professor X went to their separate ways, the next thing that is likely to happen is the formation of their own teams- X-Men and the Brotherhood.