Have you ever tried to prove the existence of morality, to yourself or other people? It seems easy and intuitive, until you actually try. Among academics, it's actually very controversial. First of all, you'd have to figure out what epistemology you'll refer to, in proving that morality exists: what are the rules you're appealing to, in demonstrating moral knowledge? Science has nothing to say about morality, and that's the epistemology we use to describe everything that exists in the physical world. Even math, which relies on constants is hinged on our perception of constants in our environment. Empiricism is inescapable.
The only other epistemology you can appeal to is pure logic, or as academics say, "apriori knowledge". There are problems with this. Basically, pure logic paints a cohesive picture of the world, where all the puzzle pieces fit together. However, in the absence of hard evidence, how do you know the picture is accurate? Reflects reality?
Many well-respected idealists, like Noam Chomsky, argue that morality doesn't require a justification: that its existence is a "brute fact". That seems silly to me, though. If Noam says that the existence of morality is a brute fact, and I say the existence of Santa Clause is a brute fact, how can Noam distinguish between what he thinks is his true claim, and my false claim to brute factedness? Either he can't, or if he can... it's not a brute fact anymore.
Anyway, we haven't even started to describe morality yet. All we've done is contemplate the rules for what would constitute knowledge OF morality, and it's a mess.
Then, once you try to describe what morality is, you end up describing the weird, spooky abstract blueprint that demands we behave one way, or another. It would be unlike anything else that exists, and it's precise nature depends on what you, yourself believe to be the nature of the obligation. So, for example, a utilitarian would describe morality in a way that differs from someone who believes in God's Command, or an egalitarian, or someone who believes in moral cultural relativism, or pragmatism. Whatever morality is, it sounds a lot like religion... Your version of the spooky abstract blueprint sounds plausible to you, but all the other ones somehow sound ridiculous...
Sorry, I ramble about this stuff. However, if anyone is interested, I suggest you read about moral error theory. It's an academic version of Moral Nihilism. They don't teach it very well in university, because most profs who teach morality believe in it. Makes sense really. You wouldn't expect to find many atheist priests, either.