Both parties are equally responsible for any unpaid credit card balance. If the primary accountholder defaults on the credit card debt, the card issuer will seek payment from the cosigner. Also, if the primary accountholder makes late payments, they could damage the cosigner’s credit score. Even if, as a cosigner, you are never required to repay the debt, your liability for the loan/credit could keep you from getting other credit you apply for because lenders will include the cosigned credit in your debt-to-income ratio. For these reasons, consider any request to cosign a loan or other type of credit account very carefully before you agree.
It can also be challenging to remove your name as a cosigner on an account. The creditor has no incentive to assume greater risk by removing an additional party (you) who could be collected from or sued for any unpaid debt. If the credit card issuer is not willing to remove your name, your only option would be to close the account, but for that, the primary accountholder's permission might be required. If the account were closed, you would still be responsible for the unpaid balance if the cardholder did not pay it off, but new charges could not be made.
Contact the credit card issuer for more information.