My favourite example, a table of Marriages with exactly two attributes: Husband and Wife. Both attributes are candidate keys because clearly we don't want to allow the same person to have more than one marriage simultaneously. So which key is "primary", husband or wife? Does it make any real difference if I pick either or even both of those as primary keys?
It would certainly seem to make a real difference. If the husband is the primary key, wives could still have multiple husbands, and vice versa. This would be a tricky one and subject to obvious questions like is the record deleted upon end of the marriage. If not, people remarry. As I don't ever have to expect to maintain such a table, that's as far as I will take these thoughts.
I would chime in, however, that I agree that the original post could have included some thoughts on the matter, newness not withstanding.