Your teacher is wrong!
They are assuming something that is not in the schematic, that the 0V rail is also ground to the CRO. What I think they are warning of is that if you connected a CRO (Oscilloscope) across the SCR, and one side of the oscilloscope was grounded through it's power cable, the voltage might be shorted out along the oscilloscope probe cable, through the oscilloscope circuits and back through the mains cable and power supply to your circuit. None of that is made clear in the circuit you show. I understand their concerns but technically, as long as the trigger voltage is placed across the gate and cathode, and there is sufficient voltage between anode and cathode, the SCR will conduct.
It is common practice to use SCRs in circuits where the the cathode is the load side, in fact I've just done it in a pump control unit and I confirm it works perfectly.
Brian.