Three vectors in three-dimensional space, no one of them a scalar multiple of any other, can still be linearly dependent. Why is pairwise non-proportionality not enough?

A. Because the third can lie in the plane spanned by the first two.

The counterexample settles it: among (1,0,0), (0,1,0) and (1,1,0) no vector is a multiple of another, and the third is the sum of the first two. Pairwise checking asks about one other vector; dependence asks whether any non-trivial combination of all of them vanishes. Independence does not require orthogonality either, (1,0) and (1,1) are independent and not perpendicular.