Israel never promised that the safe zones would not be bombed. These zones were meant to protect civilians from the bulk of the ground fighting. Nothing more, nothing less. Hamas is still present in these "safe" zones, they are fighting rockets from there, keeping hostages and their commanders in these places.

Israel did not target people moving South. Hamas themselves have blown up and shot people trying to flee in order to prevent their "human shields" from leaving. Conveniently, they then blamed Israel, even though we have an IED that looks nothing like an Israeli bomb on video.

It is true that fleeing your home is never easy and that the conditions in the South are terrible, but being poor and alive in a tent is still better than being with your possessions in your home (but dead) in the North.