You make a good point. To an extent I am sympathetic with ESRI's plight, because it is the nature of GIS to unite various disciplines, including mathematics, computer science, and geography. These disciplines have developed differing technical terms for similar things and conflicting terms for different things. For instance, common important words like "union" and "merge" mean many different things, depending on the discipline; in relational database theory, a "view" is something quite different than a way to look at a map; while "line," "arc," "polyline," and "segment" have all been used for a similar concept (of a one-dimensional geometrical object described by a sequence of points occuring along it). Thus, ESRI people have somehow to master and unite these concepts and, at the same time, continue to evolve their software to reflect a growing and more diverse set of users and an ever changing set of software platforms and data models.
That being said, the definition of "line" Dan pointed us to is downright sloppy. Given ESRI's leadership in this area, it would be nice to see them move towards clearer, more precise terminology and definitions in their literature.