Can one of the non-Christians on this forum explain to me why moral good exists in the universe?
Then why does Moral Evil exist?
I think good and evil can be understood in terms of man's purpose.
Religion can be understood as man's search for meaning, for the answer to the question, "Why am I here?" Sometimes, I think, the reason non-religious people mock religious people is because some religious people not only claim to know the answer for everyone but insist on cramming their perspective down other people's throats.
I've recently posted on this subject in a couple of other threads. You may find these interesting:
http://www.religiousforums.com/forum/2385387-post34.html
http://www.religiousforums.com/forum/2379035-post165.html
Basically, "good" can be thought of as describing what furthers man's purpose for being here, and "evil" can be thought of as what frustrates man's purpose for being here. If, like the Christians and others, you believe that man's purpose is to become a more loving individual, then "good" describes that which promotes this development and "evil" describes that which inhibits this development -- an application which, I think, leads you to the conventional notions of what these words mean.
You don't need to be a Christian, or even a "religious" person, to use this approach to understanding good and evil. I'm not sure what you intend by the word "moral"; are you thinking in terms of duty or obligation? Most people seem to understand the word this way, though I don't think that's necessary. As before, I think you can understand "moral" in terms of what is beneficial to man's purpose for existence.
This framing of "good" and "evil" lends itself to a non-relativistic understanding of value without the necessity of being judgmental. I think the reason you see many people denying the existence of an absolute standard, and saying that good and evil are only relative terms, is because they fear being judged. However, you don't need to believe in judgment to think of good in absolute terms; all you have to believe is that man has a purpose for existence.
It is well worth understanding that to deny the existence of absolute good is the same thing as saying that man has no purpose, i.e. that life is meaningless. That is the conclusion toward which all such relativism leads.
Hope this offers you some clarity.