Why is net torque zero? 
A kid of mass $M$ stands at the edge of a platform of radius $R$ which can be freely rotated about its axis. The moment of inertia of the platform is $I$. The system is at rest when a friend throws a ball of mass $m$ and the kid catches it. If the velocity of the ball is v horizontally along the tangent to edge of the platform when it was caught by the kid, find the angular speed of the platform after the event.

The solution says that net external torque is zero and proceeds as follows. Conserving angular momentum, $\text{mvr} = [ I+(M+m)r^2]\omega$ and then they found out $\omega$ quite easily.
My question is why would the torque be zero? Isn't the guy on the platform catching it? Wont he experience a tangential force (due to which there is a torque on the platform)?
 A: The external torque for the system consisting of the boy, the ball and the platform is $0$. The torque you mentioned is an internal torque.
Notice that the angular momentum conservation equation includes the angular momentum of all the 3 components mentioned earlier.
Internal torque cannot change the angular momentum of a system as internal torque is provided by internal force (in this case the action-reaction pair between the boy+ball and platform) which always come in action-reaction pairs at same perpendicular distance from axis of rotation and equal in magnitude.
A: The main condition for Conservation of Angular momentum is that

When the net external torque on a system is zero about a point then there is no change in angular momentum of the system about that point.

You mentioned the equation that led you to the desired result. If you focus on the equation carefully, you will notice that the "$mvr$" term is the angular momentum of the ball and not the man (since the man is initially at rest).
And then you equalised that angular momentum of the ball with the final angular momentum of the man, the platform and the ball , which truly indicates that the system you considered includes the ball, the man and the platform.
Once you chose them as your system the tangential force which will act on the both the ball and the man  becomes internal force in the system and if you revisit the definition of Conservation of Angular Momentum, you will definitely say that why do I need the torque of the tangential force on the man ?
