After watching the Effective Java video I noticed that boxed primitives types support only four of the six comparison operators which <, >, <=, >= and don't support == and !=.
My question is why boxed primitives don't support all operators?
They do support == and !=. They just don't do what you're expecting.
For references, == and != tell you whether two references are equal - that is, whether they refer to the same object.
class Thingy {}
Thingy a = new Thingy();
Thingy b = new Thingy();
System.out.println(a == b); // prints false, because a and b refer to different objects
Thingy c = b;
System.out.println(b == c); // prints true, because b and c refer to the same object
This applies to all reference types, including boxed primitives:
Integer a = new Integer(50);
Integer b = new Integer(50);
System.out.println(a == b); // prints false, because a and b refer to different objects
Integer c = b;
System.out.println(b == c); // prints true, because b and c refer to the same object
Now, references don't support < or > or <= or >=:
Thingy a = new Thingy();
Thingy b = new Thingy();
System.out.println(a < b); // compile error
however, boxed primitives can be auto-unboxed, and the unboxed primitives do support them, so the compiler uses auto-unboxing:
Integer a = new Integer(42);
Integer a = new Integer(43);
System.out.println(a < b);
// is automatically converted to
System.out.println(a.intValue() < b.intValue());
This auto-unboxing doesn't happen with == or !=, because those operators are already valid without auto-unboxing - they just don't do what you expect.