Overriding equals for CopyOnWriteArraySet.add and remove

I have classes like below

class A {
    @Override
    public boolean equals(Object other) { return true }
}

Class B extends A {
}

Class C extends A {
    @Override
    public boolean equals(Object other) { if ((other != null) || (other instanceOf B)) return false; }
}

In my main() I have this following code
Set<A> mySet = new CopyOnWriteArraySet<A>();

mySet.add(C);
I want mySet to contain C at this point

mySet.add(B); // #1
I want mySet to contain C & B at this point

mySet.remove(B); // #2
I want mySet to contain C at this point

I want to create a global queue where if object C exists in the queue B should be allowed to be added but not the other way around. So before #1 I am looping through the elements inside the set doing element.equals(B) with add on false.

But 1 is calling B.equals(C) which is returning true and so mySet has only one C object after this line

2 is again calling B.equals(C) which is returning true and removing the existing object C. Shouldn't it be C.equals(B) in this case? I am expecting this line as no-action

Is this some wrong use of CopyOnWriteArraySet?

Thanks for looking

HashSet is the correct collection for my case. It won't call equals while adding elements unless there is hashCode match. That way I can still use my equals methods for my specific purpose.