Fresh ATmega328P chips have their fuses set to run the CPU at 1MHz, using the internal on-chip oscillator. And the SPI interface used for serial programming needs the SCK frequency to be less than F-CPU/4 = 250kHz.
I'm not sure ArduinoISP takes any notice of the avrdude -B flag, but it it runs the SPI clock at 16MHz/128 = 125kHz so that ought to be ok...