Because vector spaces have a purely algebraic definition; geometry is not involved. This has its merits, studying a subject from an abstract, or postulation, point of view is helpful because it reveals the underlying mathematical structure but on the other hand, much of the geometric underpinning of the physical situation is missed. A good example of how relying too heavily on the algebra, with a limited understanding of the actually space is evident in an online lecture on linear algebra I once came across on mit's open course ware. In the first lecture, the professor was attempting to demonstrate a linear space with its corresponding elements (points) to his students on a white board; what a row vector was, what a column vector was, ect. but it quickly became apparent how difficult it actually is to draw a three dimensional vector space with no understanding of perspective and an adequate frame of reference (perspective). In short, what is easily written down in an algebraic equation is not so easily translated to real space without geometric considerations. Analytical geometry, in my opinion, should be an aid to geometry, not vise versa. It is not a matter of one over the other, it is an understanding of each subject to the same extent.
