According to the Law Dictionary, freedom of expression is the right to say what you want through any media, as long it doesn't harm the "character of reputation" of another individual. Freedom of expression is protected in the U.S. by the first amendment.
Especially with the rise of the internet, freedom of expression may allow for the easy spread of false information or lies. One example is the idea that vaccines lead to autism, a piece of misinformation that is dangerous and yet does not harm the character of any particular person. While it might be protected speech, it is untrue and can lead to unvaccinated children getting or transmitting preventable diseases.
Further, freedom of expression can often lead to defamation of character. Though perpetrators may later be forced to retract their statements, the damage may already have been done.
Freedom of expression protects speech that some argue can incite physical violence against other groups, such as hate speech towards an ethnic group leading to killing members of that group or violent pornography encouraging violence against women.
Freedom of expression creates its own paradox: a society doesn't truly have freedom of speech if people are not allowed to make assertions that are distasteful or unpopular to the bulk of the population, yet these statements can be hurtful to others.