The child didn't do anything illegal, and in this country we do not visit the sins of the parents on the sons.
First off, this whole question is based on a hypothetical - what if Mexico denied citizenship to children born of Mexican parents outside of Mexico. I don't think there's any nation on earth that would ever do that, so it's a moot point.
I agree that it's a hypothetical, but it's still useful in exploring exactly what we're talking about. It's not likely, but it's conceivable.
Consider "The Terminal" - lousy movie, but interesting thought. The Tom Hanks character was left without a country - his home nation no longer existed to take him back. That situation is certainly possible.
And before somebody accuses me of blending reality and fiction, the film was based on a true story.
Either way, the child isn't being punished, but simply not being rewarded. There's a difference.
Here I must emphatically disagree. Citizenship isn't a "reward," it's a right. Not a treat for the government to grant or withhold on a whim.
What makes you say it was factual? According to the web site, it was purely fictional http://www.theterminal-themovie.com/main.html