Peaches come in two varieties: freestone and clingstone. As you might expect, freestone peaches, which tend to be larger, have fruit that practically falls off the pit (or "stone"). Clingstone, in contrast, will literally cling to the pit, making it more difficult to twist and pull. If you have freestone peaches, you will be able to cut the peach with a paring knife all around its vertical center, making a circle around the pit, then pull the two hemispheres apart, pop out the pit, and slice the fruit. When working with clingstone peaches, I find it easiest to simply slice pieces of the fruit off the sides, working around the pit in quadrants to get as much fruit as possible.