I am reading more on second derivatives and something is baffling me. Nearly every page that talks about vanna(really just a handful) all say calls and short puts have positive vanna and short calls and long puts have negative vanna. why is this? If I am long a call, yes I want the IV to keep going up to increase the value of the call. This makes sense. If I am short a put, I don't want IV's to go up, therefore shouldn't I want vanna to be negative?
Similarly, for gamma, long puts and calls are positive gamma. I don't understand why vanna is different.
Also, these articles don't distinguish between ITM and OTM. A call option that is ITM will have delta go up as IV goes down.