The NEC (National Electrical Code) book states that grounding wires should be run verticle or horizontal and that diagonal runs may cause arcing. Why would diagonal runs cause arcing?

What section of the NEC states that?

Really. I know the code pretty well and this is news to me.

Did a search for the word "diagonal" in the 2008 edition of the NEC, it shows up only once in the entire book, on page 70-69 in Section 225.19 (B), and is not relevant to the question.

So, the NEC 2008 Edition is not the source of the information stated by EST081.

I will suspect he/she came across something regarding lightning protection, as the installation of "grounding" cables are to be installed in a particular fashion to help with discharging a lightning strike.

All we can do is wait for EST081 to get back with more detail.