If you have high arches,
a.
your feet roll inward when running
b.
you require shoes with more stability
c.
you need shoes with more cushioning and flexibility
d.
you should not wear running shoes

High arches or pes cavus have different causes, it may be hereditary or congenital or it can be caused by disease which affects both muscles and the brain (neuromuscular) or can be caused by a trauma in the nerve.  One way to treat high arches is by wearing shoes with more cushioning and flexibility as this will help ease the pain and also improve walking.