Do use public inheritance to model substitutability. (See Item 37.)
Even if you don't need to provide a substitutability relationship to all callers, you do need
nonpublic inheritance if you need any of the following, in rough order from most common (the first two points) to exceedingly rare (the rest):Item 8)
If you need controlled polymorphism. That is, if you need a substitutability relationship, but that relationship should be visible only to selected code (via friendship).