in this dictionary bag is used more often than suitcase
Agreed. I suggest "bag" be accepted here.
Why is "My suitcase is green, it isn't red" wrong?
The second clause doesn't use any form of 'to be'. It's just 'green, not red'.
This sounds almost identical to Ukrainain, Моя валіза зелена, не червона. Moja waliza zelena, ne czerwona.