The reason why libel and slander laws worked was in part due to broadcasters having contributory liability that would hold them liable for broadcasting someone else's libel or printing someone else's slander. This long-standing principle - that the law does not chase pointers - is something the Internet was exempted from. CDA 230 created a new category of entity that is neither speaker nor publisher and thus exempted from defamation liability[0].
Also, the law itself is actually quite weak for very obvious 1st Amendment reasons. It has built-in exceptions designed to keep it from becoming a censorship tool. However, the context in which that law exists has made the exceptions wide enough to drive trucks through.
You see, CDA 230 alone would not have dynamited the foundations of libel or slander law. Back then, the entities shielded by these safe harbors were supposed to just be web hosting providers. But technology moves on, and now we have Facebook and Twitter, which act almost identically to broadcasters except without the liability. And since they've pushed everyone to make everything public, that makes everyone a public figure[1].
If you are a public figure, it is harder to be defamed. This should be obvious, if I say Donald Trump has a narcissism problem or just mis-state the size of his wealth I should not have to defend a multi-million dollar lawsuit from him[2]. However, if I, say, get defamed by someone and respond to them on Twitter, that makes me a public figure now - which means the bar is also raised for me as a plaintiff. This is how Elon Musk got away with calling one of the Thai cave rescue divers a pedophile, for example.
[0] DMCA 512 does the same with contributory copyright liability, though with the extra step of having to give anyone with a registered copyright total censorship powers over your platform in order to get the liability exception.
[1] Technically this is a "limited-purpose public figure", which basically means "you aren't a public figure, but you stuck your nose in the debate, so for this particular time we're going to act as if you were one".
[2] Not like it stopped him - the US court system has very few ways to stop a baseless suit before it is filed.