The Chinese never really say goodbye. In fact, there isn't really a word for goodbye...The Chinese just say "till we meet again" or Zai Jian. If you go on a long journey, the traditional greeting is "have a safe journey". It is not hard to see why. Most Chinese believe in rebirth which lends much hope that all does not end with this life. If someone passes on, you express this wish that you will meet them again - as friends, as relatives or maybe even as your most hated enemy - to continue where you left off. I am really writing this as a way of internalising the "goodbye" I have to say to a loved one.
Men of science will rubbish the notion of rebirth. But then, men of science also rubbish the notion of a place with pearly gates called heaven. In fact when we say goodbye to someone, we don't really think "god be with you" which is where the origin of the word goodbye comes from. According to web sources, the phrase "god be with you" has been shorted since the 16th century to its current form. Interesting. The point is, if you believe in this notion of rebirth or that there is an afterplace called heaven, you could say to someone who is dying, "I will see you yonder" or that "Let's hope we can meet as friends, as family when you come back." When you don't have such belief systems, there is just that added intensity to the finality.
Saying goodbye is always hard. Saying goodbye to someone you know won't be around for much longer, is even harder. You can't say "have a good journey" to the other end. Those who don't believe in god or any thing remotely resembling any kind of regurgitation of the soul or a recycling or the mental continuum (one that goes on and on for countless lifetimes) believes that's just it, end of life - finito. No meetings later, as enemies, friends or relatives.
Which is why I made a stand years ago to never really be in a position of regrets with people you care about; especially your loved ones. I ring my mom everyweek to say "hello" and gossip. Most of the time, there are gripes over the phone, over this and that. Most of the time, I nod and agree, or add to the drama. Most of the time, I try to make every time spent with mom, like it is going to be the last one.
Saying goodbye in words is hard. Much harder than I ever thought. It is easier to not say all the things you want to say. It is easier pretending that all is well. It is easier just expressing all the things you want to say in actions - like doing fun things and extending the pleasures of this samsaric life. So perhaps goodbye really just is pointless, and I won't say goodbye anyway.