Actually President Obama corresponded with Hillary via her private server. She was his secretary of state and the next person in line for the Democrat party, as presidential candidate; rigged primaries. Anything that comes from the office of the President is classified. Why do you think Hillary had to erase so much data even at the risk of disobeying a Congressional order?? You don't break a direct order to hide yoga discussions. Comey pardoned Hillary as part of the cover up strategy; plan B. So Hillary was able to erase and not worry about any negative outcome.
The question is why use a private e-mail server in the first place. One reason is you don't want a public record of your doings. Another reason is a government e-mail account can be seen, internally, by government IT personal under the guise of looking for outside hack anomalies. The second reason is to avoid swamp IT, from spying on you in real time.
Hillary was the first case, since she was influence peddling for the Clinton Foundation on company time. After she lost the election, donations to the Clinton foundation dropped significantly. Ivanka, on the other hand, was aware that the swamp is embedded at all levels of government, including IT, and she was avoiding snooping eyes. Hillary was part of the swamp and was not afraid of this. The FBI and Justice Departments had her back. The FBI and Justice Department don't have Trump's back, yet. Hillary was more concerned about the Republicans having a record of her criminal activity. A private server could be made to go away if need be, which is what happened under Obama.
Another consideration is that Comey and others indicated that foreign players had hacked Hillary's server. If this was so, then any classified correspondence with Obama would have been known to the hackers. It did seem that Obama and Hillary were caught unprepared for foreign affairs things like the Russian expansion. Did they unknowingly give away their strategy to Russian hackers? Or was part of the influence peddling deal to set up an easy to hack private server, as a way to passively sell classified intel and have a buffer?