When I chop / dice a hard-cooked egg with my very-sharp knife, the density of the white causes friction along the sides of the blade, which makes the egg stick as it's going through. It's the same problem when slicing cheese, though cheese is usually not as delicate.
I know that egg slicers (like cheese slicers) utilize wires to do the cutting, thus relieving a lot of the friction as they pass through the egg or cheese. However, from watching YouTube vids of people using egg slicers, they appear very awkward to use.