Morality isn't the sort of thing you'd come up with on your own, because it doesn't make sense. Somehow, we all agree that these are the things we should do, yet none of us actually want to do them. And this spans independent cultures across the world.
Just for one example, if you do something wrong and aren't caught, not only is there something inside you telling you it was wrong, but there's also a sense that you should confess and make it right. And the only way you can get past that or suppress it isn't a logical argument that you can make for not having to confess and apologize, but rather rationalization that it wasn't wrong in the first place (not "it's okay that I hurt him" but rather "after all, who really got hurt by this?" or even "he deserved it").
Or how about courage? Courage means doing something you really don't want to do, often something that flies in the face of your own sense of self-preservation (which should be the strongest instinct humans have), yet you understand it's the "right" thing to do anyway. And there's not a single society that praises cowardice, though there really should be if all morality is merely human invention.
First of all, someone else (perhaps even someone here) had a pretty good response to that - We'd think it pretty illogical if someone stood on a coastline and said, "How can you believe in land? Look at all the water out there!"
But to be a bit more analytical, the best explanation I've heard of it is that God lets evil exist to give everyone a chance to see how bad it is for everyone. As a parent, your goal isn't to just tell your kids "Don't do that," right? You want them to understand WHY they shouldn't do it...and sometimes that means they suffer the consequences. And would anyone think all that much of a God who smacked down anyone the instant they did something contrary to his will, just because "God shouldn't allow that"? We'd all think that was pretty unfair, even tyrannical, wouldn't we?
The Christian answer to the problem of evil is that God gave all his creation free will, because free will means the potential to do great things, since you've also got the potential to do some pretty miserable things. C.S. Lewis (and probably many others) pointed out that an ant can't really be good or evil, a dog can do some good and some bad, and a human can do a great deal of good because they also have the potential for so much evil. God doesn't want automatons that obey him because there's no other choice; he wants fellow beings that worship him because they desire to. And when there's that refusal, whether it was Satan originally, or Adam near the start of Creation, or even individual people making choices in their own lives, the lesson comes not from quelling that desire to sin whenever it arises, but to teach better behavior through the consequences of worse behavior.