Why would I use a shredding service instead of just recycling?

For Security! To extract the scrap value from office paper, recycling companies use unscreened, minimum wage workers to extensively sort the material under unsecured conditions. The "acceptable" paper is stored for indefinite periods until there is enough of a particular type to process. The sorted paper, still intact, is then baled and sold to the highest bidder, often overseas, where it may be stored again for weeks or even months until it is finally used to make new products.

There is no fiduciary responsibility inherent in the recycling scenario. Paper is given away or sold and, in doing so, a company gives up the right to say how it is handled. There is, also, no practical means of establishing the exact date that a record is destroyed. In the event of an audit or litigation, this could be a legal necessity. And further, if something of a private nature does surface, the selection of this unsecured process could be interpreted as negligent. For these reasons, the choice of recycling as a means of information destruction is undesirable from a risk management perspective.

Any recycling company that minimizes the need for security has its own interests in mind and should be avoided.

The courts have ruled that once you place your material into a trash can, recycling receptacle, or dumpster, you lose all privacy rights to that information, no matter how sensitive or proprietary it is. Even if this is your trash can.  The laws on public domain protect the people taking the information - NOT YOU! You may even be held liable for negligence if the discarded material does harm to someone.