There is no consensus on what hate speech is or why it ought to banned or even whether it ought to be banned at all. I will define hate speech as speech that is created or promoted out hatred of a particular individual, group or class of people. Promoting hatred harms society and hate speech is banned because of the harm that it causes. Hate speech laws fail to accomplish their objectives because they are based on unexamined assumptions.
Promoting or encouraging hatred harms society. Hatred is a passion and all passions inhibit rational discourse. Hatred is not necessarily wrong, but when that hatred is directed at people, it treats something good (the person) as if it were evil instead. When one person hates another, it is impossible for the two individuals to trust one another. When such hatred becomes widespread, it can break and fracture civil society. In extreme cases, it can be rational for a hated group (such as Jews historically) to fear for their personal safety.
The simple and seemingly obvious solution to this problem is for the government to ban hate speech. If hate speech did not happen, then none of the results of hate speech would happen either. We would have safe and unified societies. The problem is that there are a number of assumptions involved. The first assumption is that government can reliably recognize hate speech. The second assumption is that banning hate speech will cause it to vanish. The third assumption is that the mere absence of hate speech means that none of the results of hate speech will be present either. Each of these assumptions can be contested.
Hate speech is not necessarily easy to recognize. There are sincere people who believed in the past that blacks are mentally inferior, that Jews ought to die for Christ-killing or that women ought to be protected from the evil world by men. These sincere people did not have these beliefs because of hatred. They had these beliefs because they thought they were true. Just as in the past, so it is today. Many people today have beliefs that they believe are true and others believe are hateful. But they simply do not have these out of hatred. So how could the government distinguish between these people who they will not prosecute and others who espouse the same beliefs out of hatred? Nor is this the only problem. There are also those who promote scientifically correct studies on race or differences in gender out of hatred. So even true beliefs can be promoted out of hate.
Banning hate speech may simply cause it to move underground. In Germany, holocaust denial is a crime. Yet neo-Nazism has become quite popular in Germany. Many of them have simply found new ways to promote their beliefs. University campuses in the US often have speech codes that ban such speech. This simply leads to the radicalization of these groups and the polarization of university society.
In those places in which banning hate speech succeeds such as in small, easily policed environments those who promote hatred either leave or find other ways to express their beliefs. These other ways include less obvious slights, isolation, ridicule and other forms of social stigma.
Since there is every reason to reject the assumptions of hate speech laws, examining other alternatives is a good idea.