Scarborough Fair is a very old song indeed, maybe going back to the 17th Century and even then it may reference an even far older song from Scotland. The theme of the song is contentious, and even more contentious is the lyric to it. Whereas it's fairly clear it's about a man playing hard to get by getting his ex to perform a series of unlikely and even impossible tasks, the number of verses and styles of verse vary so much that hundreds of different versions of it exist, mostly defined by the verse count and subtle word alterations.
Paul Simon heard the song on a tour of England, the story goes, and lifted his version from a folk singer named Martin Carthy, whom he had to recompense after failing to accommodate him in his credits. (The story goes on to say that Carthy never got anything from it, being swindled by a middle man) To set a counterpoint, Simon took another song of (maybe) his named Canticle (which means it ought to be sourced from a hymn not found in the Psalms, but we'll let that slide) and alternated lines from each other in the song.
Sadly for me, it does tend to let itself down badly on the lyric front, with one song about true love fair and the other being a fairly ham-fisted yearning against warfare released at the time of the Vietnam War which was doing no one much good. Maybe the sentiment was fine in itself, but juxtaposed within the frame of an old and simple song it does feel pretty contrived, striving maybe too hard to make it work as art and not just a fine tune. I'd rather hear about her finding an acre of land between salt water and the sea strands than about Generals ordering their soldiers to kill and to fight for a cause they've long ago forgotten. One works as poetry, whereas the other just sounds like contemporary worthy rhetoric.
Nevertheless, Paul Simon's (or some say Art Garfunkel's) counterpoint melody is really beautiful and definitely has its merits. I've tried to keep it restrained. In case you are wondering why the rain plays throughout, it's because every time I worked on this tune it started raining outside. I ended up miking up the sound and playing along to it. It seemed like the right thing to do, maybe making a third counterpoint concrete out of it in the process.