The answer is consistency. Moral absolutism requires consistency which obviously isn't found in the "it's okay in that case because god wanted it" answers. However, absolutism is found in the following: One doesn't initiate force because when one accepts that it's right to initiate force one must also accept that it is right to have force initiated upon oneself.
To remain consistent, if you believe that murder is okay then you must also believe that it is okay for someone to murder you. If you believe that stealing is okay then you must also believe that it is okay for someone to steal from you.
So how can morals exist without a god? Simple, I don't want someone to murder me so I know that murder is wrong. I don't want someone to sleep with my wife so I know that it's wrong to sleep with someone else's. I don't want someone to burglarize my home so I know that it's wrong to break into another's house and steal from them.