Inheritance hierarchies have their issues, and raganwald touches on them, but there's a strawman argument here.
(Incidentally, raganwald, I've noticed this about all your OO articles. You seem to have a bias against class-based design. It's causing your essays to be less brilliant than they could be.)
Fundamentally, you can think of inheritance as a special case of composition. It's composition combined with automatic delegation.
In other words, if you have A with method foo() and B with method bar(), "A extends B" is equivalent [1] to "A encapsulates an instance of B and exposes 'function bar() { return this._b.bar(); }'."
This is very useful when you want polymorphism. Writing those delegators is a pain in the butt.
More importantly, it tells us how to use inheritance safely. Only use inheritance when 1) you want to automatically expose all superclass methods, and 2) don't access superclass variables.
Now, JavaScript does have the specific problem that you can accidentally overwrite your superclass's variables, and that's worth talking about. But I think that saying "inheritance is bad" goes too far. The article would be stronger if talked about when inheritance is genuinely useful, the problems it causes, and how to avoid them.
Edit: In particular, I want to see more about polymorphism. Polymorphism is OOP's secret superpower. Edit 2: I'm not saying polymorphism requires inheritance.
[1] Not quite equivalent.