This does not compile in C++:
class A
{
};
class B : public A
{
};
...
A *a = new B();
B *b = dynamic_cast(a);
As the other stated: The standard says so.
So why does the standard says so?
Because if the type isn't polymorphic it may (or is? Question to the standard gurus) be a plain type. And for plain types there are many assumptions coming from the C backwards compatibility. One of those is that the type only consists of it's members as the developer declared + necessary alignment bytes. So there cannot be any extra (hidden) fields. So there is no way to store in the memory space conserved by A the information that it really is a B.
This is only possible when it is polymorphic as then it is allowed to add such hidden stuff. (In most implementations this is done via the vtable).