I'm on Sequoia so stuff may have changed. For me there is a sidebar (menu bar at the top, View, Show Sidebar) and in the that is a favorites (menu bar at the top, Mailbox, Goto Favorite Mailbox)
Might want to get this moved to the MacOS forum....
This thread is just screaming for a screenshot. To my knowledge, Favorites can't be deleted or hidden, only opened or closed using the little triangle that appears when you hover over it. You won't see "All Inboxes, "All Drafts", or "All Sent" though unless you have more than one email account set up. Show us what you're seeing.
Here's the screenshot (scroll down for full view). The "All Mail" is something I managed to add, to no effect whatever. And I don't see a Favorites option. I've read restoring the Mac, but that didn't change anything. I'm still receiving mail as I always did, but the search function for "All Mailboxes" would be immensely helpful to me.