It also occurs in the form "neither rhyme nor reason," and occasionally, "neither reason nor rhyme."
The reason it's become a set phrase is probably because it appears in Shakespeare, "As You Like It:"
"Was there ever any man thus beaten out of season,
When in the why and the wherefore is neither rhyme nor reason?"
I don't understand why this phrase means what it means, particularly not the word "rhyme," and most people who use the phrase don't, either.
Some other fragments from Shakespeare that have become set phrases include "the be-all and end-all," "eaten me out of house and home," "put it in a nutshell." As with many phrases from the Bible, they have simply entered the language and we use them without thinking of their origin.