Family sharing not recognizing my method of payment PayPal

PayPal isn't a valid payment method for a Family Share : Payment methods that you can use in the iTunes Store, App Store, and iBooks Store - Apple Support

If you're using Family Sharing and you're the family organizer, you can use the following payment methods:

• Credit and debit cards
• Some additional payment methods available in select countries or regions (Alipay, China UnionPay, mobile phone billing, TrueMoney)

You can also create an account for a child under 13³ using these payment methods, with the exception of mobile phone billing.

I don't know the details of how Paypal works, and Apple doesn't provides the 'why' for many of its requirements. One thing that is clear for something like Family Sharing to receive acceptance by the various companies (not just Apple) involved is to ensure the members really have a close 'family' relationship. One way to demonstrate this is to make sure one person is open to bearing the financial burden of purchases made by other members. I don't know if it is possible to set up a dummy account in Paypal that would mask it actually being several unrelated people doing the payments.

Yes, but that's my point. For those other things Apple doesn't really care who is making the payment really, as long as they get their money. I think for Family Sharing they want to really put somebody on the spot as a way of making sure sharing is only between a highly trusting or financially controlled group such as a family might be. You are more unlikely to share your music with a group of casual acquaintances if you have to put your credit card on the line for any purchases they may make.