I am not saying that inheritance is mandatory to OOP. I think "mandatory" is too strong of a word here. As I said, OOP means different things to different people and I am okay with that.

Speaking for myself, OOP is a way to orchestrate programming on a large scale. To grow software without growing the frequency, severity, and difficulty of bugs and without growing costs associated with new features is the desired result. Component-ized architecture takes great steps to achieve this result. For this reason, I view OOP as being some combination of: message passing, encapsulation, and polymorphism. I do not believe this is a complete view of OOP, nor that there is no viable alternative view of OOP.

Polymorphism is often implemented as at least inheritance of interface in statically typed languages. Without polymorphism you don't get dynamic dispatch, especially open to extension at runtime.