MacArthur neither wrote nor said, "Old soldiers never die; they just fade away." In his Farewell Speech to Congress he paraphrased the song, (anon) "Old Soldiers Never Die". Here is the close of that speech:
"And like the old soldier of 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 light to see that duty."

The entire speech is extremely moving and deserves to be in books of famous speeches (MO).