which I manage, and show me where the "Make Public" option is located.
I can't see it myself because I am not a manager, but you should find a check-mark for that when editing the profile.
If you open the Immediate Family or Family group list you will also have a "Make This Profile Private/Public" link in the actions column if this is an operation you want to do on multiple profiles.
I noticed that I can't find Make Public / Make Private from the profile but can find it in the List view of a family reached either from the bottom of a profile by pulling up the family, or from the main menu under Family > List and making whoever you chose the focus person.
I think that might be what you mean, Private User?
OK, I went back to Abraham Brown's profile and found his "Immediate Family."
Clicked on "View All," which led to Abraham as the "Focus Person."
However, there's no way to make his profile "Public" or "Private" there.
So I clicked on his wife, Mary.
Found her "Immediate Family" and clicked on "View All."
With Mary as the "Focus Person" you can see Abraham's name and a button to make his profile "Public" or "Private."
(Does anyone find this a rather arcane way of reaching a destination?)
Private User - I'm glad that you raised this topic because I had a similar problem, having made some close family profiles public due to the default setting, and not finding a way to change the privacy setting on the profiles themselves until I found this option.
I'd have to experiment a bit to understand what's available when, but it seems that the Actions option to change close family members from public to private and vice versa disappears after the profile is created except through this route. Of course I am talking about profiles that you and you alone manage. Once you invite them and they manage their own profile, it's their decision.