Actually, the explanation is
simple:
War is a federal matter.
Education is a state/local matter.
And, constitutionally, the federal government has very little control over how states spend money on education. In fact, the federal government has no direct power to legislate educational systems. The federal government's contribution to education is dwarfed by the states. (Perhaps in part because federal taxes are so high, that the state can't squeeze much more out of you.) So the next time you want to complain about funding for education, talk to your state and local legislators. Your congressman and senator can't help you much (except by agreeing to cut your taxes--tangential and unlikely support).
It always cracks me up to hear politicians running for federal office talking about education reforms. This is mainly posturing. There's really very little they can do about it.