A long, long time ago — before the advent of straightedges — if there was a need to determine a straight line, the tool typically employed was a stretched out thread made from linen. And this connection to the linen fiber — no need to make things complicated — is in fact why we call it a line.
I like a well executed line as much as the next person. And I also happen to love linen cloth. So when I recently took out the sewing machine to piece together a linen shirt, and as I made one seam after the other of magic lines down the fabric, I was in tactile heaven.