The First Amendment is commonly understood as protecting the right to free speech. But the First Amendment does not impact the ability of private citizens and organizations to punish or limit speech. This is why it’s permissible for a private employer to fire an employee for engaging in speech the employer disapproves of – private employers have the right to manage their employees as they see fit.
The situation grows more complicated when the government is the employer. Like any other employer, the government has a legitimate interest in maintaining efficient offices and agencies, which often requires managing and disciplining employee speech. At the same time, however, public sector employees have a protected right to free speech under the First Amendment.
The law attempts to balance these two interests noted above by differentiating between private and official speech. The First Amendment only protects government employees when they are speaking as a private citizen about matters of public concern. If the government employee’s speech is instead part of their official job duties, they can be disciplined or fired for what they say.