Polynomials of degree at most 2, 2x3 matrices, and arrows in the plane are studied as one subject. Why is it worth proving a theorem about "vector spaces" rather than proving it three times about three concrete objects?

B. Because the proofs would be identical, using only the shared properties.

Try the experiment: prove the theorem for polynomials, then for matrices, and the two arguments turn out to use nothing about either, only that you can add, scale, and land back inside. The abstraction is the recognition that the proof was never about the objects. Solutions of a linear differential equation form a vector space, and every theorem was waiting for them.