Poincare Hopf: possible vector fields on the 2-sphere

Question

According to the Poincare Hopf theorem, we know that the sum of the indices of the critical points of a flow over the 2-sphere is 2. I conclude that we can have one critical point having index 2, or two critical points having index 1 (e.g. the flow of west winds). But doesn't the flow of east winds over the sphere create two critical points of index -1? Or is it not possible to have such a vector field on the 2-sphere?

Answer 1

The flow of east winds over the sphere that you wrote seems the following picture.

The index of this flow must be $1$, not $-1$. Then the sum of indices of critical points is $2$.

The index $-1$ is the following picture.