There is never an excuse to disown a child. There are good and justifiable reasons to give a child up for adoption.
There are situations in which a child becomes so out of control and dangerous to self or others that parents need to bring in some sort of help — even to the point of legal structures such as filing a Youth at Risk Petition. But disowning a child, in the sense of rejecting her or him (refusing to recognize him or her) for reasons having to do with the child’s nature or actions, is never justified. No matter what a child has done, s/he is still your child. You can criticize their behavior, and even agree that they suffer the consequences of their actions. Even when it means incarceration. But that child is still yours. And in many cases your parenting has contributed in some way to the child’s problems — even if you did the best parenting you could. You don’t get to run away now and say, “That’s not my child.”
More importantly, as a parent, it is never acceptable to give up on your child. They may have done something so horrendous that they are incarcerated for life. But you still have the spiritual responsibility to be their parent and offer them your presence in their life. Every soul is potentially redeemable.