Get an Apple Music Student Membership - https://support.apple.com/HT205928
The above article has a section on Family Membership and students. It may not address exactly your question but should provide some fundamentals. It seems to imply you can have a student membership when part of a family, but it is a separate subscription. This does not explain your friend not being able to join the family in the first place unless there's something odd about having a student membership that is not covered in the article. In that case you may need to ask Apple:
Contact Apple for support and service - "See a list of Apple phone numbers around the world."https://support.apple.com/HT201232
You say these are "friends". I hope they are good friends. One of you will have to make your credit card open to all the others in order to set up a Family.
How iTunes Store purchases are billed - https://support.apple.com/HT201359
For the Family Organizer:
Payment methods that you can use with your Apple ID - Apple Support - https://support.apple.com/HT202631 --> "Payment methods for Family Sharing
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)"
Also your own credit balance from gift cards, but only for your own purchases.
