My answer assumes your child was an authorized user of the credit card account in question, and was not a co-signatory.
A credit card issuer can, and in many cases must, report the activity on a credit card account on the credit reports of the primary cardholder and all authorized users. However, only the primary cardholder is legally liable for charges on the account.
When the account in question was paid on time and the balance was low, this account helped boost your child's credit score. Given the longevity as an authorized user, this account jump-started your child's ability to get credit.
Now that the account is in default, the reverse is happening — this account is dragging down your child's credit score. Is that fair? That depends on your perspective and the strength of the account.
What can you do about it? Remove your child and any other authorized user from this account immediately. After you do so, your child may need to dispute this derogatory entry.
I hope this information helps you Find. Learn & Save.