Perhaps we could consider geodesics in a curved 7-dimensional space whose projections onto a plane might form the shape of a kitten.

Lines also, by definition, have no beginning or end. They're defined by a simple equation like y = mx + b. Good luck drawing one of those with any ink.

Lines, by definition, are also infinitely thin and extend infinitely far. By definition, they cannot exist in our world of atoms. :)

When people use the word line to refer to something in the real world, there are often some unstated assumptions baked in. I guess it's important for the consultant and the client to have the same understanding of what those unstated assumptions truly are.