I'm by no means an expert or qualified, but here's my thoughts.
I believe there are a few factors at play:
The first is the perception that the information carries some threat to their lifestyle or reputation, e.g. an adult who views pornography or a cheating spouse, for both of whom this causes that initial concern of the threat of exposure (and we may over-estimate their impact upon exposure as a form of impact bias).
Second, narcissism: they're worried their actions could be considered damaging to their image and believe that those who invade their privacy (a government / a social network selling aggregate topic stats to marketers, etc.) would take great delight in exposing their behaviour. Of course they wouldn't, but people generally like to think their own lives are of importance to everyone, and so why wouldn't their "important" secrets be of importance to everyone else?
First I'll throw in that the person may remember the last time they were burnt by their privacy being invaded by others (such as malicious gossip), which may serve as a negative reinforcement to not infringe on others'. You remember the last time and how much it hurt you and don't wish to knowingly inflict that on someone else, especially for no personal gain.
There is also the thought that if we do a good deed that others will reward us for it...or if we deem ourselves to have done something selfless, we derive gratification from it. This is also closely linked to narcissism. I read something ages ago that inferred there is never a truly selfless act, as we often do it to feed our ego.
If legislative changes are made to protect privacy generally (e.g. social networks' usage of private messages are tightly controlled), then we also could benefit from this, so there is also potentially some selfish gain in concern over other people's privacy, and we can project how we are annoyed at a particular company doing something with our data on "behalf of a friend".
Finally, if we believe strongly that our own "privacy" is important (when in reality most people are just referring to morally questionable behaviour they would like to suppress), then we also see others' as just as important as some way to justify that our own belief in the protection of our privacy is founded. A "bias blind spot" and "confirmation bias" appear in the list of cognitive biases.