Private inheritance causing problem in c++

There's nothing wrong with your logic, except that it's missing one point:

private inheritance basically means that only the inheriting class (B in this case) knows that it inherits from the base A. That in turn means that only B can make use of all the privileges that come with this inheritance. One of these privileges is to be able to cast B* to A*. The function foo() doesn't know about B's inheritance, so it cannot perform that cast.