Yes, the doctrine of Original Sin, which some Christian denominations emphasize far too heavily, makes some children feel guilty for just being born.
A more healthful teaching would be that most people have both good and not-so-good tendencies. Skilled parenting can bring out the good qualities, with or without JC. A typical person is born with the potential to have a conscience as an adult. Sociopaths are the exception, but they are only something like 1% of the population.
As moral beings, we have the power to make the right choices sometimes, and to make the least bad of the bad choices at other times, with or without JC.