There are a few reasons your pencil might break during sharpening. If you've dropped or damaged the pencil, the lead inside the pencil might have broken and sharpening it is just revealing the already broken lead. In that case, you might want to invest in a pencil pouch to protect your pencils. Another option is using an electric pencil sharpener that can do smoother, more even sharpening with the helical blade rather than a simple manual blade. Many electric sharpeners also have auto stops that prevent you from oversharpening, another reason your lead might be breaking.