PET vs CT?

Had an appointment with oncologist,asking for PET. He seems not happy with it and saying he didn't see any reason for doing it. It would show no change from the CT before survey. I asked for the difference in between, he said the PET can only detect 1cm and CT can detect .5cm, also he mentioned PET/CT is not necessary according to
the standard he showed me online.

Is that true? But any way he agreed to do CT