I know it's a new concept for you, but a call and a put (European, with the same strike and expiration) are related through put/call parity. If the data shows different IV for these, it means the underlying is being modeled incorrectly.Puts and Calls have their own respective IVs.
Are you meaning the IV for Put and Call for the same strike has to be identical?That would be wrong!
Or do you mean something else? Just give an example demonstrating your point of view.
That would be wrong!