Why is it not a good practice to synchronize on Boolean?

private Boolean isOn = false;
public void doSomeStuffAndToggleTheThing(){
   synchronized(isOn){

This is a terrible idea. isOn will reference the same object as Boolean.FALSE which is publicly available. If any other piece of badly written code also decides to lock on this object, two completely unrelated transactions will have to wait on each other.

Locks are performed on object instances, not on the variables that reference them:

I think your problem is more with synchronized itself than with sync'ing on Booleans. Imagine that each Thread is a road, where statements (cars) go one after another. At some point there may be an intersection: without a semaphore collisions may happen. The Java language has a built in way to describe this: since any object can be an intersection, any object has an associated monitor acting as a semaphore. When you use synchronized in your code, you are creating a semaphore, thus you must use the same one for all the roads (threads). So this problem is not really boolean-specific because only two Booleans exist, this problem happens every time you synchronize on an instance variable and then point the same variable to a different object. So your code is wrong with Booleans, but is equally dangerous with Integers, Strings and any Object if you don't understand what's going on.

I am not able to understand the reason why we should "never synchronize on Boolean"

You should always synchronize on a constant object instance. If you synchronized on any object that you are assigning (i.e. changing the object to a new object) then it is not constant and different threads will be synchronizing on different object instances. Because they are synchronizing on different object instances, multiple threads will be entering the protected block at the same time and race conditions will happen. This is the same answer for synchronizing on Long, Integer, etc..

// this is not final so it might reference different objects
Boolean isOn = true;
...
synchronized (isOn) {
   if (isOn) {
      // this changes the synchronized object isOn to another object
      // so another thread can then enter the synchronized with this thread
      isOn = false;

To make matters worse, any Boolean that is created through autoboxing (isOn = true) is the same object as Boolean.TRUE (or .FALSE) which is a singleton in the ClassLoader across all objects. Your lock object should be local to the class it is used in otherwise you will be locking on the same singleton object that other classes might be locking on in other lock cases if they are making the same mistake.

The proper pattern if you need to lock around a boolean is to define a private final lock object:

private final Object lock = new Object();
...

synchronized (lock) {
   ...

Or you should also consider using the AtomicBoolean object which means you may not have to synchronize on it at all.

private final AtomicBoolean isOn = new AtomicBoolean(false);
...

// if it is set to false then set it to true, no synchronization needed
if (isOn.compareAndSet(false, true)) {
    statusMessage = "I'm now on";
} else {
    // it was already on
    statusMessage = "I'm already on";
}

In your case, since it looks like you need to toggle it on/off with threads then you will still need to synchronize on the lock object and set the boolean and avoid the test/set race condition:

synchronized (lock) {
    if (isOn) {
        isOn = false;
        statusMessage = "I'm off";
        // Do everything else to turn the thing off
    } else {
        isOn = true;
        statusMessage = "I'm on";
        // Do everything else to turn the thing on
    }
}

Lastly, if you expect the statusMessage to be accessed from other threads then it should be marked as volatile unless you will synchronize during the get as well.