There is so much talk and noise going on in the modern world, that people, seem to have lost their knowledge over the necessity and value of silence. This is not to say that silence in and of itself, is necessarily always good, rather, that sometimes we should actually gaze at one another in silence, we should contemplate while silent, we should consider more carefully our words before not remaining silent, and we should understand that sometimes words cannot adequately convey what we are feeling or thinking, so sometimes silence is indeed, best.
The thing about talking is that it brings attention to the person that is doing the talking, and attention is something that a lot of people want to have, most of the time. This then means that in our conversations, too often, people aren't actually have a dialog, but more of a monologue of one person speaking their part, and then another person speaking theirs, in which neither is really interested or paying much attention to what the other person is saying.
So too, the more talk that there is, in which each person says something, the longer the talking continues and continues, so then, when your response instead is silence, it has a tendency to slow the talking down considerably or even to lead it to its conclusion, especially when certain people won't stop talking until they get the last word in, but what of it, if you have already moved on, anyway.
Additionally, not everything that comes to mind is worth speaking of, as some things that are thought of, are most definitely inappropriate and even mean to say, so they really should not be said. Also, when someone is very passionate about something, of which your basic feeling about it is fairly neutral or mildly against it, there isn't any good reason to have an argument or to get involved by speaking your mind, for your opinion is reasonably quiescent, so why not leave it that way, and let the other person's passion, eventually burn out.
While there are definitely times to talk and to speak out, that would imply also the corollary that there are definitely times to be quiet and not to speak out, of which, since words have power, both good and bad, it would behoove us to more often keep silent about saying things that are hurtful and spiteful, for it doesn't do us any real good for saying them, and the person receiving them, most definitely would agree.
Once a word is spoken, you cannot take it back, for it has left your mouth, whereas what you think in silence, most definitely can be taken back, for no one is the wiser of it. That is why we should value the discretion that silence provides for us, in addition to the fact, that if we talk less, people might indeed listen to our words more, because we will not have the possible reputation of being one that prattles on about things that do not really matter, but rather may well be known instead, for being pithy, incisive, and wise.