So... reasons why it's so bad:

1. voldemort has a kid with Bellatrix. Doesnt make sense at all. Voldemort is incapable of feeling love, so why would he feel the desire to hook up with Bellatrix? One explanation is that he wanted a child as his heir. However, he thinks that he is immortal. Why would he need an heir if he plans on living forever?

2. This kinda leads on from my first point but NO ONE notices that Bellatrix is PREGNANT. Like, when Harry, ron and hermione get caught by snatches and are brought to Malfoy Manor, bellatrix would have been pregnant with delphini. But no one says a thing? Like, she tortures hermione, and throws a dagger at the just as they're apparating away. She throws the dagger with perfect force and precision, and even tho it didnt hit the trio, she managed to kill dobby... it's pretty difficult to pull those stunts off when you're pregnant.

3. They completely messed up Harry's personality. He shouts at McGonagall and says that she wouldn't know what being a parent is like, deeply hurting her feelings. The Harey from the books wouldn't hurt her like that.

4. The time travel. In the books, time travel isn't meant to create alternative realities. However, in the cursed child, it does.

5. Cedric diggory becomes a death eater. Why would losing the tri wizard tournament motivate a guy like him to turn dark? Seriously, it doesnt make sense. He's a frickin hufflepuff and has demonstrated his good nature loads of times in the books.

6. The trolley witch. Why is she a monster it doesnt make sense.

There are loads more reasons, but it's been a couple years since I last read the book so I cant think of anymore at the top of my head. Plus, it's like 4am now so I'm pretty tired.

Anyway, I hope this helps :)