The eggs are probably too fresh.Use eggs that are at least five days old from their packing date for hard boiled.Boil them and then run the cold tap over them.Then tap the eggs all over to crack the shells, then hold each egg under a slow trickle of running water as you peel the shell off, starting at the wide end. The water will flush off any bits of shell that cling on.
If I could just add, that it's best to put a colander in the sink to catch the fragments. This way there's less delving in the plughole - a horribly fiddly job.