I want my macbook air to log me off and show the login screen every time I close my laptop. In system preferences I have checked the "require password immediately after sleep or screen saver begins" box, and when I close or computer or command to sleep, it still won't log me off.
MacBook Air 13", macOS 10.14
Do you really want to do that? That would potentially involve data loss as anything you had open at the time would presumably terminate without saving.
What's wrong with just requiring you to authenticate with your password after closing the lid?
Automatic login
Choose Off to require users to log in whenever the Mac restarts.
To automatically log in a particular user when the Mac restarts, choose the user’s account name and enter the user’s password. This option is useful if the Mac has only one user and is always in a secure location. If security is a concern, automatic login should be off.
Note: If FileVault is turned on, automatic login is disabled.
Display login window as
To let users choose from a list of usernames when logging in so that they don’t have to remember their usernames, select “List of users”.
To require users to enter both username and password when logging in, select “Name and password”.
Show the Sleep, Restart and Shut Down buttons
Shows these buttons in the login window.
Show Input menu in login window
Lets users choose the language macOS uses after login.
Show password hints
Displays a password hint in the login window. The hint is shown during login if the user clicks the question mark in the password field or enters a password incorrectly three times in a row.
Show fast user switching menu as
Enable switching quickly between users from the menu bar. Choose how users are displayed in the menu bar from the pop-up menu.
Use VoiceOver in the login window
Allows VoiceOver, the screen reader built into macOS, to be used during login.
Note: When zoom is enabled in Accessibility Zoom preferences, you can use zoom in the login window to make the password field appear larger. In the login window, press Option-Command-8. To increase the zoom, press Option-Command-Equal sign (=). To turn off zoom, press Option-Command-8.
Allow network users to log in at login window
Lets users log in to your Mac using accounts on a network account server that your Mac is joined to.
Accessibility Options
To select options that make it easier to log in to your Mac, click Accessibility Options. See Turn on accessibility options in the login window.
Network Account Server
To join (or connect) your Mac to a network account server, click the Join or Edit button. The button is labelled Join if your Mac isn’t connected to a network account server. It’s labelled Edit if your Mac has an existing connection.
Add 
and Remove 
To add a new user or group, click the Add button , then enter the information for the new user or group. To delete a user or group, select it in the list, then click the Remove button . See Delete a user or group.
Lock 
Locks or unlocks Users & Groups preferences. Click the lock icon to unlock it, then enter an administrator name and password.
Do the setting as per screen shot .
Automatic Logoff when laptop closes
