I don't have to tell anyone about anything that I witnessed because if I don't feel comfortable about it, then I am not obliged to tell. People should be given the right to be silent as they see fit. They should not be forced to tell everything that happened in their personal lives, or the life-threatening secrets of their friend, or if a family member is a criminal.....Etc. To explain this more clearly, let me give you an example.
Patty's friend, (not even that close) Gwen, just committed a horrific crime, then killed herself. Investigators are searching for possible motives, and questioning Gwen's relatives/friends about Gwen's personality, hobbies, and lifestyle. A few days before Gwen committed the crime, she told her feelings on life. These feelings could probably give investigators a good idea of why Gwen did what she did. However, Patty doesn't feel comfortable exposing her friend that much to the judgmental public, and believes even though Gwen did something very awful, the motive is best not revealed. Patty has the right to remain silent. She can ignore the reporters, the news, the investigations all she wants.
It's all about making people feel comfortable. People have the right to not speak out if they feel like they are being pressured, or if they have their own private reasons. Nobody can pressure you to expose a secret or give valuable information. It's according to your own beliefs and how you think speaking out or remaining silent will affect society.* Besides, if we did not have the right to remain silent, then I am sure many people such as Patty will be extremely uncomfortable and unsatisfied with the government. People as a whole will be angry at the government because they do not need to tell everything about themselves or what involves themselves to the public. Imagine a world where no one has the right to remain silent about certain happenings that are best kept private! Speaking out is good, but sometimes silence is needed just the same. Anyways, overall, we really do have the right to remain silent. Sorry for the wishy-washy explanation.
*I am leading into "no" territory here.
Yes, we really do have a right to remain silent, because a confession can be suppressed if it is not made voluntarily. If someone does not want to speak to the police, they are free to leave. If the police abuse that privilege, they are subject to penalties and loss of employment, as well as civil penalties.