Why is density considered to be a property of matter but length is not?

Here is a non-scientist's view. Density is a ratio, and as such it is an abstract expression of the nature of a certain kindof matter. Density is indepenent of how much or how little matter you are talking about. Density is the amount of mass per a unit of volume of the material. Length, on the other hand, is a characteristic of a given piece of measureable material, independent of the make-up of the material. Every rigid physical object has some linear measurement that can be considered length. The length of the object can be modified without changing in any way the nature of the matter. In a given reference frame, the density of a given kind of matter is constant.