You're right, in many cases, hate speech and bullying are obvious and can be easily spotted. But there are always grey areas and disagreements where eradicating hate speech and bullying can also end up getting rid of speech with valid political dimensions.
One sort of obvious case where important speech was classified as harmful is facebook's recent spat with the prime minister of Norwary over them censoring the famous photo of "Napalm girl," a young, naked Vietnamese girl running naked in the streets from a Napalm attack.