To make this purchase, ask your organizer, (name), to provide a new payment method.

I had this problem too. The strange thing was that I could purchase from my account on my computer and devices, but my wife using the family sharing could not. She would get the prompt for the security code, and then get the message, "To make this purchase, ask your organizer, ____, to provide a new payment method." Didn't seem to make sense, since the same payment method worked for me. Turns out the account had an old expiration date for the credit card. Apparently Apple ignored it for my purchases, but it was an issue when adding someone else to the account. After fixing that, it worked.

You are not being asked to change your info, if I understood correctly - your organizer is. Why, no idea, but suspect there is some problem with his payment method or payment. So either leave family sharing or ask organizer to update.