Excluding comfort and similar eating which is less likely to apply to breakfast So the trigger for hunger is when your blood sugar is low, after a fast over night, your blood sugar is being maintained by the reserves stored in the liver. How large your stores are in the liver and how full they were at the start of the fast is what will control how hungry you are in the morning. If you have small stores or go to sleep with them depleted (say last meal at 5pm) then you'll get hungrier quicker than if you have large stores and ate late.
Your metabolism does indeed change if you have breakfast - but only if you start doing some physcial things, the glucose that starts arriving in the blood from breakfast is used directly encouraging sugar burning at a lower intensity of exercise than if you'd not had (where you'd've just used fat for the energy required)
It's not actually unhealthy or otherwise to not have breakfast, however if you're someone who normally needs breakfast (because of your smaller store in the liver.) then you will become much more likely to then become very hungry and reach for the very quick fix calories that are often unhealthy.
If you regularly don't have breakfast, your body will adapt to carrying more calories in the liver - that's how the body works - so it will become more and more self fulfilling and the people won't need breakfast. Exercise also increases storage in the liver.
As others have said, some (but far from all) obese people do have problems with hunger and satiety and what's motivating them to eat is different. But in general not being hungry for breakfast is perfectly reasonable, as long as it doesn't cause very low blood sugar later because when you are hungry, food isn't available.