As an example: what if you're gay, or a pregnant teen, or into the swinging lifestyle, or a liberal, or any other thing that you might not want people to know?
The article cites an example of how Target outed a pregnant teenager to her family by starting to send her ads for diapers and baby supplies. Her father was angry at Target (because he thought they were promoting teen pregnancy, and not just reacting to it) until he found the truth.
What if she lived in a household where her family would kick her out for having gotten pregnant?
Another example of data leakage: when Google Reader decided to go 'social' and let you share your feeds, they turned on public sharing by default; I read one blog post afterwards about a man who followed several liberal blogs even though his family was extremely conservative. As a result, his family saw that he was reading 'that trash' (paraphrasing) and they ended up having a huge argument (and, AFAIR, making their next holiday awkward and uncomfortable).
It's also not hard to imagine targeted advertising popping up on your computer, making other people (family members? coworkers?) jump to conclusions (correct or not) about you or your lifestyle, or violent spouses noticing ads for abuse counselling based on your google searches.
Even aside from the 'it's not their business' angle, these automated data harvesting and management systems are completely impersonal; they have no idea how much you share with others already or what you don't want other people to know. When even following a liberal blog can get you in an argument with your family, there's an argument for not trusting companies implicitly to handle your data in a responsible manner.
So to answer your question, what you gain from opting out is control over your life, information about yourself, and how other people perceive you.