So you got your Instagram account, and started connecting with your friends and family. Went on vacation, posted the pictures, your friends and family like the photos. With more and more followers, you start getting that feeling that you want your pictures private... So you set your profile to private (and only the followers can see it), and you are safe. Right? Not Exactly.
Let's start from the end. If there is something that needs to be private just lock it down at home, in a safe, encrypted drive and hide it behind a secure password.
I'll go into the shallow details, the thing is, the more followers you (USER A) have on Instagram the higher the risk of one of those followers (USER X) is compromised, i.e. has a very weak password that a hacker or a data mining website can use. These accounts serve directly (it is a hacker's account following you), or indirectly (the account is compromised with a weak password and the user don't know it) to leak the picture of your account which they are following.
Of course, on some social media you (User A) can keep the image settings as private, but a more tech savvy (USER Z) at some point can with a very low probability to get a grab of your data from the servers, the same thing that happened with the celebrities in late 2014.