What does the first amendment have to do with slander, libel, and defamation?

The first amendment protects you from the government prosecuting you for the content of your speech.

The first amendment does not protect you from the results of your speech, like someone deciding they don't like you because of what you said. That person is free to dislike you for what you said and the first amendment has nothing to do with it.

Similarly, if you say things that are untrue and cause damage to others, you may be held civilly liable for the damage if they sue you and convince a jury that you lied with knowledge and intent to lie. The first amendment has nothing to do with this.