News is just out that the use of personal email accounts in the State Department goes back at least to the tenure of Colin Powell, and that he also dealt with "classified" material in emails from his private account. It would not surprise me at all if it went back to whichever Secretary of State sent the first email from his office.
All of these high-level State Department types say they use private email because they don't trust the reliability or security of the government email system. They especially don't trust its internal security, that is, they suspect that far too many people within the State Department can read their stuff. Secretaries of State are also often major political players who deal with all sorts of partisan political subjects, for which they are supposed to use private accounts. For such people the line between official business and party business is often hard to draw. I suspect also that since several previous Secretaries used private email accounts, each new Secretary sets up such an account as a matter of prestige; damned if they won't have every perk their predecessors had.
The real problem here is not the use of private email accounts by State Department officials, it is the government's ridiculous habit of classifying all sorts of public business as "secret." For obvious reason we don't know what is in most of the emails that deal with "classified" material, but we do know in one case. This concerns emails Clinton and some associates exchanged about American drone strikes in Pakistan. Officially, it is a secret that we even have drones in Pakistan, even though the news media report on them all the time. In this case the email exchange started because one of the parties sent along a news account of such a drone strike. Even though the subsequent exchange was all about a media report, the government thinks that since it deals with the "secret" topic of drones in Pakistan, it is ipso facto classified.
Sometimes just thinking about all the crap our government tries to keep secret makes me want to vote for Bernie Sanders.