How do I log out of ICloud email?

If your apple mail application is signed with Apple ID and in the system preferences , in the location iCloud the Apple ID is signed in , then iCloud mail is configured .

To sign out from iCloud account , take cursor on top menu bar - mail and click on quit the mail .

If it is an IMAP account and you are the administrator you can change the admin password and don't share with your family members see this article Change the login password on Mac - Apple Support

But they will stop using the Mac , but if you don't want to be done don't set up an IMAP and icloud account account .

You can delete the imap account and iCloud account from the location system preferences - internet accounts click on subtract sign to remove them , see this article Add or remove email accounts in Mail on Mac - Apple Support

And then start signing with you web mail account and iCloud account on their respective server link like www.icloud.com and example on gmail account whatever service like yahoo etc is configured .

Its your choice either to change login password or remove the accounts .

But if delete the iCloud account make sure you generate iCloud Keychain verification code before clicking on minus sign , later if you plan to set up the iCloud accounts you must at least have that code in record ( if you are using secondary authentication id and iCloud Keychain is set up ) , if you wish the process of generating code it can be explained .

You could change your admin password as suggested above and then reserve that account for your use. Then go to System Preferences/Users & Groups and set up another user account for everyone else to use. That would keep your emails and other data secure from anyone being able to use it.