The reality is that I never had any clue what these Secrets were, unless it revolves around the fact that sometimes my family prefers Rice-a-Roni versus the Indian branded basmati rice (the horror!). But whatever they were I wouldn't tell. Moreover this advice/scolding to hide The Secrets began from the age of 7 and has continud well past my mid-20s. (I imagine it will go on forever, but my empiracal evidence is limited to how old I am).
The reason of course for hiding The Secrets is because once others know, The People will Talk. Who are these People? Any whom are they Talking to? Why do these People even care about what goes on in our lives? While valid, these are not questions to ask parents. The sheer logic behind the questions prevents it from being a answer-worthy topic. However, in the one moment of bad judgement when a child actually asks a parent this question you usually receive a stern look and the oft-occurring Desi Parental Veto:
Hero/kid: Who would Talk about our Secrets?...I don't even remember what happened after that...
Parental Unit: Son, I know you think you're so smart, trying to be a smart Alex P. Keaton, but I've got news for you, your parents weren't born yesterday, there are things we can't explain to you
Hero/kid: But if you're so smart, why can't you explain it?
[stage directions: BLAMMO! child is smacked upside the head]