In February two innocent children, 11 and 7 year old died in an airplane crash while riding in a single engine airplane during pilot training. The airplane was flown by a student pilot and instructor. Plane crashed in Navasota, TX killing all 4 people. News story: http://goo.gl/rMsYRh
The whole concept of training flights is flying an airplane at the limits of flight envelope. During training people intentionally cause airplane to stall, roll, steep turn, and do thing that are un-typical during a passenger flight.
Furthermore, having a student doing these flight acrobatics is prone to delay reaction and incidents.
While flight instructors, who fly with students are fully aware of their risk, the children were not. Lets stop this practice of having passengers on training flights: