What is the physical cause that circulation on a closed surface is zero?

This is quoted from Feynman's Lectures:

We would like to see what happens when the loop shrinks down to a point, so that surface boundary disappears - the surface becomes closed. Now, if the vector $\mathbf{C}$ is everywhere finite, the line integral around the loop must go to zero as we shrink the loop. According to Stokes' theorem, the surface integral of $(\nabla \times \mathbf{C})_n$ must also vanish.

Mathematically, from Stokes' theorem, it can be inferred that

$$\int_{\text{any closed surface}} (\nabla \times \mathbf{C}) \cdot n \cdot da = 0.$$ But physically, what is going on that is making the circulation zero in the closed surface?

• Your equation is a mathematical theorem. It seems to make little sense to try to explain why it is true from experience. Aren't you looking for examples of its use in physics, instead? – Ján Lalinský Apr 5 '15 at 13:05
• @Ján Lalinský: Yes, sir. Actually I want the reason. – user36790 Apr 5 '15 at 13:09 