Speed can defined as the rate of distance travelled by a body.(not the displacement). So distance÷time.Also it is a vector quantity which means it not taking the value of direction..Also speed cannot be negative. Its always positive. So when a body is at rest its speed is zero.so when a body moves from one point to another,it will attain different speeds.
If average speed is zero i.e the sum of the distance will be zero(that we got from the equation).Since distance is also a scalar quantity and it wont be negative if we moves in opposite direction. It always adding irrespective of direction.So total distance travelled of a moving body can not be zero. So total average speed also cannot be zero and it will be nonzero if body is moving..