Defamation lawsuits. Right now, a bunch of people can tweet "John Doe (some public figure) beats his wife" with no verification, and Twitter keeps the tweets up, and doesn't get in trouble when John Doe's life is ruined by the false accusations.
What's more, media can then report "John Doe is allegedly a domestic abuser," citing the tweets as evidence that there are allegations that John Doe is a domestic abuser. You see this pattern with pizza gate (some dumb social media posts getting picked up by Republican news), and with Kyle Rittenhouse (dumb, false twitter posts picked up by left-leaning news). In the latter case, the news outlets have been getting sued for defamation because the reporting was damaging and so demonstrably false.
Section 230 protection for these platforms erodes all standards of truth for news.
Libel of public figures in the US has an extremely high bar. It needs to be proven that a statement was known to be false or the publication was reckless in deciding to publish the information without investigating whether it was accurate. (Initially established in New York Times v. Sullivan.)
You can of course sue for any reason but winning is another matter.
(It's easier if the defendant is not a public figure, but still, in general, it's relatively hard to win libel suits in the US.)
"John Doe" above is not a public figure - your parent's point is that social media enjoys all the advantages and power of newspapers without bearing any of the responsibility to strive for truthfulness.
In fact IMO it's even worse - unlike newspapers which would at least be embarrassed by blatant mis-reporting, sensationalist and fantastical stories are a major source of profits for social media, and they've got incentives to encourage and promote them.
Yes, most mainstream publications do strive for truthfulness (fortunately) but it's not really a requirement for 1st amendment protection and I'm sure we can think of fairly mainstream news outlets that don't let the truthfulness responsibility cramp their style too much.
Consider what social media would look like without Section 230. Could it even exist? It would need automated tools to verify the accuracy of millions of posts in real time. I doubt they could be built even with a massive budget. If you rely on user reports of inaccuracy, you'll need a huge staff to deal with everything, and will be bombarded by trolls acting in bad faith.
Ironically, given all his complaining, if Section 230 didn't exist, Twitter would have no choice but to ban Trump. He'd be an absolute nightmare in terms of liability.
Furthermore, it's not just about social media which didn't even exist in its current form in 1996 (the Web barely did). Rather Section 230 was more focused at the time on things like ISPs and hosting providers. So it's not just about Twitter and Facebook. It's also about things like individual web pages.
What's more, media can then report "John Doe is allegedly a domestic abuser," citing the tweets as evidence that there are allegations that John Doe is a domestic abuser. You see this pattern with pizza gate (some dumb social media posts getting picked up by Republican news), and with Kyle Rittenhouse (dumb, false twitter posts picked up by left-leaning news). In the latter case, the news outlets have been getting sued for defamation because the reporting was damaging and so demonstrably false.
Section 230 protection for these platforms erodes all standards of truth for news.