Warren in Lancaster, PA
You can use any kind of oil you want as long as you are using the stone regularly. However if you use a low grade mineral oil and let it sit unused for a period, it will get gummy. The reason is that the mineral oil is a mixture of oils of various weights and the lighter more volatile oils evaporate over time leaving the heavier oils behind. The sperm oils is of uniform viscosity so this is not a problem. Honing oil is more refined than just any mineral oil. That is to say the oils that comprise it are in a narrow range, so more uniform like the sperm oil. There is a reason why you pay more for honing oil than just "mineral oil".

If you are using the stones daily and constantly adding fresh oil, the oil does not get gummy.