No, just the opposite. You are entitled to claim the EIC (if you are otherwise eligible), based on that child (I added something to my original reply earlier to explain that). "Non-dependent for EIC only" is the correct designation
The father, most likely, claimed something he's not allowed; probably EIC. Ask him to review his return. He can also not claim Head of Household or the dependent care credit. If so, he will have to file an amended return and you will have to mail in your return.
You could delete the child, for now, and e-file. Later, after the father has amended, you could file an amended return to add the child back for EIC.
