Overriding public virtual functions with private functions in C++

Question

Is there is any reason to make the permissions on an overridden C++ virtual function different from the base class? Is there any danger in doing so?

For example:

Answer 1

There's no technical problem, but you will end up with a situation where the publicly available functions will depend upon whether you have a base or derived pointer.

This in my opinion would be weird and confusing.