In the source novel, several reasons were given for choosing Ender and his lieutenants at such a young age;
- Only Ender, as Commander, has sufficient empathy to understand the highly complex flight patterns used by the Buggers (the Formics) but sufficient raw aggression to fight them on their own terms. Note that they still had to trick him. Had he known that he was sending real men to their deaths, he would have balked.
We had to have a commander with so much empathy that he would think
like the buggers, understand them and anticipate them. So much
compassion that he could win the love of his underlings and work with
them like a perfect machine, as perfect as the buggers. But somebody
with that much compassion could never be the killer we needed. Could
never go into battle willing to win at all costs. If you knew, you
couldn't do it. If you were the kind of person who would do it even if
you knew, you could never have understood the buggers well enough."
- Only children have the required hand-eye coordination required to pilot and control the massed fleets.
"And it had to be a child, Ender," said Mazer. "You were faster than
me. Better than me. I was too old and cautious. Any decent person who
knows what warfare is can never go into battle with a whole heart. But
you didn't know. We made sure you didn't know. You were reckless and
brilliant and young. It's what you were born for."
- They've been breeding and selecting children for martial greatness for 50-ish years. Ender might be young but he's described (in all seriousness) as being quite literally one the greatest military minds of all time, regardless of his age
"Does it ever seem to you that these boys aren't children? I look at
what they do, the way they talk, and they don't seem like little
kids." "They're the most brilliant children in the world, each in his
own way." "But shouldn't they still act like children? They aren't
normal. They act like history. Napoleon and Wellington. Caesar and
As to why they didn't choose Mazer or Graff to lead the Fleet (above and beyond the reasons above) is that Graff is a general who's never fought a single space-battle and Mazer is considered an oddball whose small "strike force" scored an insanely lucky last-ditch blow against the Bugger fleet. He's never been fully trusted by the administration because he's never been able to sufficient explain to those in charge exactly what happened. It's only when Ender arrives that he finally encounters a mind that is on a par with his own:
"The videos of the Second Invasion, when they were destroying our
fleets out in the comet shell." He began to call them up and display
the buggers' patterns. "Show me the queen's ship." It was subtle.
Ender couldn't see it for a long time. The bugger ships kept moving,
all of them. There was no obvious flagship, no apparent nerve center.
But gradually, as Mazer played the videos over and over again, Ender
began to see the way that all the movements focused on, radiated from
a center point. The center point shifted, but it was obvious, after he
looked long enough, that the eyes of the fleet, the I of the fleet,
the perspective from which all decisions were being made, was one
particular ship. He pointed it out. "You see it. I see it. That makes
two people out of all of those who have seen this video.
In the film they kinda gloss over this, simply noting (in the intro)
The International Fleet decided that the world's smartest children are the planet's best hope. Raised on war games, their decisions are intuitive, decisive, fearless. I am one of those recruits.