It's a bit of a winding road to get to those concerns, but it has to do with how ZeroNet works. A site can be published to ZeroNet by an individual user, but those who then view it become a "seeder," just as BitTorrent users can seed parts of files shared over the network. By default if you access the site, you download up to 10MB of data from it to share through ZeroNet, though users can choose to download and seed more if they're so inclined.
The real problem here, though, is that 8Chan is a website filled with the worst garbage one can find on the internet, including child pornography. While the site technically says child porn and other illegal content isn't welcome, it's well-known as a place where one can find these things. And thanks to how ZeroNet works, it's possible that such illegal material could be downloaded to someone's computer and then distributed from there.
Of course, you'll need to actually view that content before it gets downloaded and shared from your computer... so it's entirely possible to view 8Chan and just don't look at child porn. But given the chaos that is 8Chan, you really are taking a bit of a risk viewing the site at all over ZeroNet, as you never really know what manner of horror you might come across (and then accidentally distribute). "If you visit a site, then it's [sic] get downloaded to your computer and you start serving it to other visitors," ZeroNet told The Daily Beast. "So yes, it could happen, but if you find something problematic that you don't want to host you can delete the site any time using the web interface."
You'd think it would be easy enough to just not view child porn or other illegal material, but some 8Chan / ZeroNet users are still worried. "Yeah but what if i dont notice the pedo," a ZeroNet user said in response to the idea of just avoiding potentially problematic material. "id be storing cp on my drive, so if my computer got seized for whatever reason im fucked."
Ultimately, this ZeroNet version of 8Chan doesn't seem terribly sustainable. Aside from the concerns voiced by users about potentially distributing illegal material, it also just raises the barrier of entry to accessing the site at all. While the 8Chan administrators try and bring the proper site back online, it's not surprising that some of its more "passionate" users are trying to find a way around it. But as a sustainable solution, it would be surprisingly if a ZeroNet version of 8Chan really catches on.