python - Why is my "if" statement not working?

I'm confused as to why the if statements highlighted aren't working. If I type "remove" or "removeall", the message I have for each message does not print.

https://pastebin.com/iawK1gyT

while user != "":
    if user.lower() != "remove" or user.lower() != "removeall":
        recipients.append(user)
        userQuery()


    elif user.lower() == "remove":
        if not recipients:
            print("You haven't added any recipients yet.")
            userQuery()

        else:
            del recipients[-1] # Removes the last item of the list

    elif user.lower() == "removeall":
        if recipients:

            print("Removed every user from the recipient list.")
            recipients = [] # Removes every item from the list
            userQuery() 

        else:
            print("Can't delete an empty recipients list.")
            userQuery()