It is right that both the action and reaction should be equal and opposite to each other. In the above case we move upward because the forces are acting on two different objects that is the ground and feet so they are unbalanced forces even if they are equal in magnitude. They will only cancel each other if they are balanced forces that act on same object. That is why Newton's third law leads to motion even when the forces are equal in magnitude and opposite in direction.
alternative solution:
earth mass dominate over human mass.