A contact profile can only be edited from the account where the contact is created. If you're unable to edit a contact, you're likely logged into a sub-account and trying to edit a shared contact that originates from the parent account.
Shared contacts are identified via a small Share icon next to the number:
To edit this contact:
- You'll need to log into the parent account and edit the original contact profile. Or;
- Export the contact from the parent account, and then import it directly into the sub-account as a new contact, making it native to the sub-account.