A spinning cricket ball has velocity both due to linear(v) and rotational motion(u). when a ball is moved forward, the air occupies the space left by the ball with a velocity v (say). When the ball spins, the layer of air around it also moves with the ball, say with the velocity 'u'. So the resultant velocity of air above the ball becomes (v-u) and below the ball becomes (v + u). Hence, the Due to this the velocity of air above the ball decreases and below the ball increases. According to Bernoulli's principle decrease in velocity increases pressure on the upper side of the ball.

So there is a downward force on the ball and because of this and it fails to follow parabolic trajectory.