Why in the Thevenin Theorem do we have to "turn off" independent sources to find Thevenin resistance
Say you connect a voltage source Va at the external terminals across which you want to find the the equivalent resistance. Now if you change the voltage Va, voltage across the elements in the network changes, so does the current. The ratio of this change in voltage to that of current, \$\Delta V/\Delta I\$ is the equivalent resistance offered by that element. 

The total resistance of a network can be calculated by replacing each element by its equivalent resistance. 


For a reistor, \$\Delta V/\Delta I\$  will be its resistance value only.
Since voltage across an independent voltage won't change (\$\Delta V=0\$), its equivalent resistance will be zero. Hence it can be replaced by a short. Similarly, independent current source (\$\Delta I=0\$) can be replaced by an open circuit. Which is basically 'switching off' these sources.
But for dependent sources, this \$\Delta V/\Delta I\$ ratio need not be zero or infinity as the value of source depends on voltage/current at some other node/branch in the network. Hence effectively it can have a non zero finite resistance to offer and hence can not be 'switched off'.