That right there *is the alignment problem*.

If I task an AI with "peace on earth" and the solution the AI comes up with is ripped from The X-Files* and it kills everyone, it isn't good enough to say "that's cheating" or "that's not what I meant".

* https://en.wikipedia.org/wiki/Je_Souhaite

It's playing a game in which the rules are a bit ambiguous if not explained.

And in reality the set of rules we would need can never be fully explained.

Alignment is the goal of having an AI system understand what we would want it to do even when the rules weren't predefined. That's an impossible task, or rather its seemingly impossible and we don't yet know how to do it.

That's the alignment problem. We intended a certain set of rules but didn't define them completely, or there were conditions we didn't consider.

An AI wouldn't have to maliciously break a rule to go wrong. The point is that the system could so exactly what it was supposed to do, it plays within the given rules but the outcomes aren't what we wanted or intended.