Why is a class allowed to have a static member of itself, but not a non-static member?

Question

class base {
public:
    base a;
};

It gives compilation error.

class base {
public:
    static base a;
};

wherea

Answer 1

Because static class members are not stored in the class instance, that's why a static would work.

Storing an object inside another object of the same type would break the runtime - infinite size, right?

What would sizeof return? The size of the object needs to be known by the compiler, but since it contains an object of the same type, it doesn't make sense.