You need new teeth or try sharpening your teeth. :-)
Whoever buys the celery in your home probably always look for the biggest bunch in the lot. Usually the large stalks are tough and more fibrous, and a darker shade of green. Always choose stalks which are light green, tight and compact. Examine carefully for seed-stems - a round stem in the place of the smaller tender stalks that should be in the centre of the celery. Celery with seed-stems are often more bitter in flavour.