Why can't we initialize class members at their declaration?

The initialization of non-static members could not be done like this prior to C++11. If you compile with a C++11 compiler, it should happily accept the code you have given.

I imagine that the reason for not allowing it in the first place is because a data member declaration is not a definition. There is no object being introduced. If you have a data member such as int x;, no int object is created until you actually create an object of the type of the class. Therefore, an initializer on this member would be misleading. It is only during construction that a value can be assigned to the member, which is precisely what member initialization lists are for.

There were also some technical issues to iron out before non-static member initialization could be added. Consider the following examples:

struct S {
    int i(x);
    // ...
    static int x;
};

struct T {
    int i(x);
    // ...
    typedef int x;
};

When these structs are being parsed, at the time of parsing the member i, it is ambiguous whether it is a data member declaration (as in S) or a member function declaration (as in T).

With the added functionality, this is not a problem because you cannot initialize a member with this parantheses syntax. You must use a brace-or-equal-initializer such as:

int i = x;
int i{x};

These can only be data members and so we have no problem any more.

See the proposal N2628 for a more thorough look at the issues that had to be considered when proposing non-static member initializers.

The main reason is that initialization applies to an object, or an instance, and in the declaration in the class there is no object or instance; you don't have that until you start constructing.

There's been some evolution in this regard. Already, at the very end of standardization of C++98, the committee added the possibility to do this for static const members of integral type---mainly because these can be used in contexts where the compiler must be able to see the initialization. In C++11, the language has been extended to allow specifying an initializer in the declaration, but this is just a shorthand—the actual initialization still takes place at the top of the constructor.