A couple of reasons. Some of them can overlap, some others are mutually exclusive.
1.- Anything that can learn might not learn the right lessons, which explains machine apocalypses in movies.
2.- The belief they steal the jobs. Under normal circumstances machines tend to replace the most mechanical and repetitive works, so to think they can become creative could create a sense of uneasiness.
3.- Since they use other people’s art to learn some get a sense of property stealing. This one is debatable, technically they create a new piece although on the other hand there’s a bit of tracing or plagiarism involved, but then again is not like the AI can still go beyond that yet.
4.- No one wants to appreciate or buy art for what it seems comes from just a tool where not actual skill and technique is involved.
5.- Sometimes is not the AI itself, but not a lot of people trust the people behind the AI’s because since it involves learning data they might feel their privacy would be violated or that companies and governments have shady intentions.
Pick your poison, reasons? they definitely exist, good reasons? I’m not sure I can be judge here.