Jill Lepore delivered a brief history lesson on the subject in the New Yorker this week: "The networks wanted Nixon and Kennedy to question each other; both men insisted on taking questions from a panel of reporters, one from each network, a format that is more generally known as a parallel press conference."
According to a Washington Post report on Sept 1, 1960, "the networks, led by NBC's board chairman, Robert W Sarnoff, proposed the two candidates join in a 'great debate' on the air." By "great debate," Sarnoff meant a head-to-head, unmoderated affair loosely rooted in the Lincoln-Douglas tradition. In fact, the word "debate," as it was understood at the time, meant that no moderator would be involved. Thus The Post referred to the first Kennedy-Nixon session as a "discussion of issues" or a "TV engagement."
New York Times columnist Jack Gould wrote on Sept. 7, 1960, that "the scheduled 'great debate' between Vice President Nixon and Senator John F Kennedy looks as if it may emerge as a spectacular news conference for two."
It did not start out that way. The Post reported on Aug. 17, 1960, that "both men look forward to the debates, and to some televised joint press interview shows, as the events most likely to influence voters." The original plan, in other words, was for the candidates to meet in different kinds of forums, some of which would meet the era's definition of debates and others that would involve questions from journalists.
By September 1 that year, The Post had more details: "The presidential candidates agreed yesterday on two face-to-face, hour-long radio and television debates, plus one and possibly two dual appearances before a news panel."
A week later, however, it appeared that the candidates were having second thoughts about debating, as Gould wrote in the Times. On September 16, 10 days before the first event, The Post reported the final outcome: "The once-contemplated 'great debate' has been lost. Now, the candidates will appear together, answering questions from a panel of reporters and with each commenting on the other's answers."
The Post went to report, citing CBS News president Sig Mickelson, that "the format was worked out with the hope of preventing 'long-winded speeches.' He added that each candidate's representative wanted a fast-paced program that would keep an audience interested. Mickelson added that the questioning by the panelists might bring more forthright answers than if the candidates questioned each other."
So there you have it. Kennedy and Nixon did not trust each other not to filibuster, so they wanted journalist moderators to probe for "forthright answers." The format has changed very little in 56 years. What has changed is our definition of the word "debate."