Why one should not eat Prasad offered to Shivling

The Shivling is a form of Lord Shiva and is one of the most commonly worshipped ones. During the month of Sawan, and even on normal days, the Prasad offered to a Shivling is usually Gangajal, milk, Panchamrit, honey, sandalwood paste, fruits, flowers, and the like. But, the fruits and flowers offered are not given back to the devotee.
Once these items are poured or placed on the Shivling during the Abhishekam, the priests just let it flow through.