Answers above are correct: both variants can be used, but the meaning is slightly different.
To grasp what's going on, remember that in English, complete Subject-Verb structures are required. They are often skipped in a colloquial speech, but they are always needed to completely "unroll" the full sentence:
If he was right, why {was he right}? If {he was} not {right}, why {was not he right}?
If he was right, why {was he right}? If {he was} not {right}, why not {was he right}?
"If not, why?" may also imply a continuation:
If he was right, why {was he right}? If not, why {do you think so}?
Something like this (sorry for my poor drawing):
↓────────────────────┐ ┌────┐
↓─────────────┐ │ │ ↓
If he was right, why? If not, why {do you think so}?
Or, simply:
↓────────────────────┐ ┌───┐
↓─────────────┐ │ ↓ │
If he was right, why? If not, why?
OTOH, "If not, why not?" is pointing directly to an original phrase:
↓───────────────────────────────┐
↓─────────────┐ ┌──↓ │
If he was right, why? If not, why not?
I think both are same. 1st one is If he was not right, why not is he right? and the 2nd one is If he was not right, why is it so? (The italicized parts are not said explicitly) – Mistu4u – 2013-01-26T08:31:55.850