The private listing setting has been redundant for some time; it was originally intended to be used when the item was 'sensitive' (eg iincontinence pads) where buyers would not want details showing up on their feedback profile. eBay stopped showing details on buyer profiles some time ago.
Some sellers use the setting by mistake but there are some out there who use it to disguise shill bidding. If you are not happy then just walk away without bidding.
