why do I have to link my Skype account with my MS account?

Signing into Skype uses the Microsoft Account of the active user. If your Skype account is already linked to that Microsoft Account, it just uses that, if not you can link it to a Skype account that you have.

So, for a family member that has a Microsoft Account on the console, but has not yet linked it to a Skype account, they should follow the flow to use an existing Skype account or create a new one.

You can unlink the Microsoft Account that is linked to a Skype Account as described here:

support.skype.com/.../how-do-i-unlink-my-skype-and-microsoft-or-facebook-accounts

Already did with no luck. I will try again, but my skype isn't linked to this account and I paid for things on the MS store using Paypal

Easiest is unlinking your wrong Skype account from your Microsoft account from your computer's browser. Follow the instructions here:

support.skype.com/.../how-do-i-unlink-my-skype-and-microsoft-or-facebook-accounts

After unlinking you can start the linking process again and pick the right Skype account this time around:

support.skype.com/.../how-do-i-merge-my-skype-and-microsoft-accounts

It sounds like there's some kind of confusion between Skype accounts and Microsoft accounts. Sign in to Skype on the web with to unlink your accounts, and then you can re-launch Skype on Xbox One to link the Skype account you want to the Microsoft account
that you use on your Xbox.

(For more information about unlinking accounts, see
support.skype.com/.../how-do-i-unlink-my-skype-and-microsoft-or-facebook-accounts)

If you need help with unlinking, go here:
support.skype.com/.../how-do-i-unlink-my-skype-and-microsoft-or-facebook-accounts

If you need help with re-linking, go here:
support.skype.com/.../how-do-i-merge-my-skype-and-microsoft-accounts