Ms. Marvel APPEARED as a guest star in issue 171. She didn't join until issue 183. Carol Danvers as Binary never served as an Avenger. Thus her status as past Avenger is null and void.
Yes, you did lie. You specifically said that Binary joined the Avengers in issue 171. I disproved it. You got caught.
Carol Danvers aka Binary was NOT an Avenger. She participated in the Avengers mission against Morgan Le Fay in Avengers Vol. 3 #1-3. Her powers as Binary were severly depleted during the event. In fact she was taken out by Justice, the New Warrior with a telekinitic blast. Her powers as Binary faded away in Avengers Vol. 3 #3 before she was inducted into the Avengers. In Avengers Vol. 3 #4 she served under the alias as Warbird, her powers as Binary completely gone.
Binary was never inducted into the Avengers.
She lost her powers in issue #3. The Beast performed tests on her and concluded that her powers as Binary were completely gone. Carol herself said she could never transform again. They then made new and weird codenames for her.
In issue #5, She and Captain America sparred together, in the training room. Cap asked her why she didn't just turn into Binary and lay waste to the droids. Warbird dodged the question because she already lost her powers in the prior issue.