Can you give me a concrete example when is preferable to use private inheritance over composition? Personally, I will use composition over private inheritance, but there might be the case that using private inheritance is the best solution for a particular problem. Reading the C++ faq, gives you an example on using private inheritance, but I seems easier to use composition + strategy pattern or even public inheritance than private inheritance.
private inheritance is typically used to represent "implemented-in-terms-of". The main use I have seen is for mixins using private multiple inheritance to build up a child object with the proper functionality from the various mixin parents. This can also be done with composition (which I slightly prefer) but the inheritance method DOES allow you to use using to expose some parent methods publicly, and allows for a slightly more convenient notation when using the mixin methods.