"I am not a man."
I don't think there's anything weird about the answer at all. Also, are you sure it doesn't accept じゃない as an alternative?
Unless this happens to be a newly added sentence, I would almost certainly have used じゃない on it before. I would remember if this sentence kept rejecting my answer, unless I've somehow never encountered it yet.
All of the following (among others) should be acceptable:
Oh so NOW all of a sudden we MUST specify 私は for this kind of statement, when I've gone through 19 levels when it's not been that way and often even deemed incorrect to do so? Make up your freaking mind, Duo!
See my answer to that in the "I am not a woman" sentence discussion. ^^