As Phil (@TheBBG) said. It is up to your carrier.
The historical reason is that the White & Yellow pages were part of what is now Telstra. Prior to 1993 their trading name was Telecom Australia.
Telecom Australia, and then Telstra being the monopoly carrier gouged for every penny they could, and used to charge customers not to have their names listed. Possibly this was because if my memory serves me correctly; in the early days actual living breathing people were responsible for manually removing details from the database Telstra provided of all of their connections. Another area did all the corrections. This is why it took so long to process and was so error prone.
Now days Telstra & Sensis still seem to be in the same monopolistic mindset where they believe they can largely ignore their customers and charge a premium for their services.
Back to your issue.... If you have a valid privacy reason for wanting to be removed, many carriers will do so for free if you approach them, as Phil suggested.