This is.....oversimplifying. There are a variety of ways to say goodbye in any language, and the one presented here is the most heavy handed Japanese has. This is saying goodbye to your family when you leave for college, not goodbye to your buddy you'll see after class. I'm seeing a lot of similar comments in other questions which makes me happy, but duolingo desperately needs some way to better communicate a cultural understanding of Japanese phrases, and not just a purely semantic one
I have heard this often, but, my native Japanese tutor used to say さようなら to me as i left my lesson each week, and he did not think it was unusual to say this.
So I remain confused on the appropriate use of さようなら. Which is to say, maybe it's not all that incorrect? Feedback would be nice!
My college Japanese professor explained that さようなら was used when you didn't expect to see someone until after a life event or extended period of time, and teachers say さようなら at the end of the school day to their class, but not in between classes. So, in your case さようならwould seem to be correct.