The contacts that you see in WhatsApp come from your phone's address book. To delete a contact from WhatsApp, you must delete the number from your phone's contacts.
After you delete this contact from your phone:
Deleting a contact from your phone's address book will remove that contact's number completely from your phone. There is no way to remove contacts from the Favorites tab without deleting them from your phone contacts.
Note: Deleting a contact does not prevent that contact from messaging you. If you would like to stop receiving messages from a number, you can block it. To learn how to block a contact, read this article.
If you would like to add a contact to WhatsApp, find out how here.
Learn how to delete a contact on: Android | iPhone | Windows Phone | BlackBerry | Nokia S60 | BlackBerry 10
Cheers,
WhatsApp Support Team