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

Another way to do this is to utilize the "Contacts" software to set up the Email, as is explained under "Help" for "Contacts", and then under "Show Topics" and then under “Composing” and then under "Create Groups" and then under "Email a Group"...

For me, the first option worked, but the second one did not work (names of all the Members of the group were displayed in the "To" field of the Email addressed to the group). I haven't yet tried the third option...

Absent that approach, in “Mail” software (version 9.2) under “Addressing”, in which, if the first box is not checked, the Email addresses are supposedly not displayed; however, that approach did not work, for me, and this additional step was successful in avoiding the display of all the addresses...