This myth has various possible origins. One is from the Greek legend of Arachne the weaver. Another is found in Navajo weaving practices. Most likely the quilting version of this myth came from the belief that Amish and Mennonite women put a mistake in each quilt because only God is perfect therefore it would be prideful to make a perfect quilt. Yet it has been pointed out by some Amish women that making such a mistake would be prideful in itself as it would imply the quilt maker believes herself to indeed be perfect.
Though some rare purposeful mistakes may have been for religious reasons it appears for others it was more a matter of superstition. In reality all quilters make mistakes, it's almost impossible to make a perfect quilt. The purposeful mistake myth prevails though, mistakes in antique quilts are sometimes said to have been made on purpose. A good line to help sell a quilt, I suspect. As making a mistake on purpose was never a common practice a mistake found in an antique quilt is unlikely to be a purposeful one.
Learn more about Amish quilt history at Amish Quilts & Quilting History: Beauty in Simplicity.