For me, if I consider it "a secret" I won't be sharing it with anyone, at all, ever (or at least until I decide I don't want it to be a secret any longer. There are "confidences", which are things we want kept within a small circle of close family members or friends Those are different from secrets.. I'll share a confidence with someone - but never a secret. Even with confidences, though, I'm very careful about what I'll share with whom; so I draw a line on any confidence I share too.
There are a lot of different things that make something "a secret" for me. Most of them have to do, I guess, with the idea that everyone has a right to privacy on some matters; but also with whether or not other people (as the famous move-line goes) "can handle the truth". Knowing how to "handle the truth" involves someone else's not being a blabbermouth, a know-it-all (who would presume to have the right to share a secret for reasons he deems important), a worrier, a person who doesn't have the reasoning ability to recognize the difference between what he's been told and "all the other stuff" he's imagined beyond that, or someone who gets something out of the secret-holder's/sharer's secret.
Sometimes we may keep things a secret only because we know someone else "doesn't know how to handle the truth". Whatever the information is, we might otherwise not see it as "secret" at all if it weren't for the fact that we know that sharing it with someone will cause one problem or another (for us or for someone else, but seldom for the person we share the information with first).
Again, though, what makes a secret a secret is the fact that we won't share it. To me, once it's shared it becomes either a confidence or else "public information" in general.