This is a short, conceptual question related to the post: Surface integral of position vector over a sphere
We have a vector field integrated over the the entire surface of a sphere of radius $a$, and this field has constant magnitude $a$ at all points on the sphere. The answer is fairly trivially $4\pi a^3$, but I don't understand why each vector pointing out of the sphere is exactly cancelled by a vector on the antipode of the sphere, meaning everything cancels out and leaves us 0. It might be something fundamentally wrong with my interpretation of a vector surface integral. Any help would be appreciated.