Pitcher faking throw to 3rd base

[rinbee]

I have read in training materials that a pitcher make fake a throw to 2nd or
3rd with his foot in contact with the rubber. He can only fake to 1st after stepping off the rubber. I had a manager complain that a left-handed pitcher cannot fake to 3rd without first stepping off. I see his point, but I have not seen any distinctions in the rules about whether a pitcher is right or left handed. Thoughts?