Answer:
"old soldiers never die, they just fade away" was a phrase taken from an old army ballad. its most well known use was when it was said by General Douglas MacArthur at the end of a speech representing the end of his military career.
He said:
"Old soldiers never die; they just fade away. And like the old soldier in that ballad, I now close my military career and just fade away, an old soldier who tried to do his duty as God gave him the sight to see that duty."
He was kicked out of the military by the president for insubordination after MacArthur voiced disagreement with his policies. The president was unhappy with MacArthur's plan to open a two front war by attacking china to end the Korean war.
The Full Song went:
Old Soldiers Never Die
There is an old cookhouse, far far away
Where we get pork and beans, three times a day.
Beefsteak we never see, damn-all sugar for our tea
And we are gradually fading away.
Old soldiers never die,
Never die, never die,
Old soldiers never die
They just fade away.
Privates they love their beer, 'most every day.
Corporals, they love their stripes, that's what they say.
Sergeants they love to drill. Guess them bastards always will
So we drill and drill until we fade away.
The simple answer is: It was a phrase made famous by General Douglas Macarthur, but probably sang by thousands of different soldiers.