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Where does this concept of “favor composition over inheritance” come from?

I have colleagues at work who claim that "Inheritance is an anti-pattern" and want to use composition systematically instead, except in (rare, according to them) cases where inheritance is really the best way to go.

I want to suggest an alternative where we continue using inheritance, but it is strictly forbidden (enforced by code reviews) to use anything but public members of base classes in derived classes.

For a case where we don't need to swap components of a class at runtime (static inheritance), would that be equivalent enough to composition? Or am I forgetting some other important aspect of composition?