Peter was afraid to be identified with JESUS because of all the turmoil prevalent in the day. Certainly, he was afraid of the various forms of punishment he might be subject too should he identified himself as one of JESUS' disciples.

With regards to why people are still afraid, I suspect it has something to do with how others view and or like us based on our beliefs. We're a society that wants to be liked and often times it becomes difficult to stand up for what we believe in due to public opinion or pier pressure.