It seems that some customers were offended that the company wanted to know whether they agreed with statements like "My partner is likely to reject me at some point unless I am better (smarter, better looking, etc.) than any other potential mate" and "I could disappear from the face of the earth and no one would notice."
Amazingly, the reporter for the news article actually managed to interview someone (a survey guy, even) who didn't see the problem with this.
The questions read like something you would find on a standard psychological profiling tool--the kind of thing your doctor might ask you to fill out before prescribing antidepressants. The point of the survey was probably to try to build a profile of Target customers in things like anxiety, loneliness, etc.
Nielsen/Netratings (the company hired to implement this gigantic brain fart) probably convinced Target that there was nothing particularly intrusive about a standard psychological assessment, and both companies overlooked the fact that if someone asks if you're worried that your wife might leave you, there's a world of difference between a therapist asking the question and a discount retailer.
Frankly, I'm astonished that this ever happened. One of the things anyone writing surveys should know is that the context of a survey makes a huge difference. Survey questions don't exist in a vacuum, they exist in the context of the relationship between the person (or entity) asking the questions and the person answering them.
Anyone who's ever asked the income question ("What's your annual income?") knows this. Asking a retailer's customers questions like "I am afraid of being rejected by my friends" is nothing short of sloppy.