Because they couldn't come through with the promised filtering technology that would prevent the trading of copyrighted material.

Napster shot themselves in the foot. They swore in court that they were not in business to promote the trading of copyrigthed material. They claimed that their primary interest was trading non-copyrighted material. They also promised that they could supply filters, and that when they did, people would still use Napster. Each of those statements was a lie, and the courts told them to put up or shut up.