How to create a private distribution list [group mailing list] in Mail.app?
Send to yourself - some mailers won't send if there's no 'To' recipient
Mail.app actually will, so you could optionally leave the To field blank - though I'd test that your ISP allows it through as well, before relying on that.

Then send to the group as BCC
BCC stands for Blind Carbon Copy, as opposed to CC which is just Carbon Copy
i.e. the recipients are hidden from each other.

Show/hide the BCC field from the View menu, or  Cmd ⌘   Opt ⌥   B  



Then enter your Group name in the Bcc field; click the drop-menu or hit  Enter  once it's recognised.
The pref you mentioned - "when sending to a group, show all member addresses" - switches between showing the field as "my Group" or "Fred, Barney, Wilma" etc