Talking about teaching humanity to mankind is like talking about teaching birdness to birds, or teaching vegetability to vegetables. Human beings are not special. Like any other order of things or beings, they have their own way of dealing with each other and they make changes (improvements?) to these methods as and when their environment requires.
The Bible, The Koran, and the Bhagavad Gita are books. Their content is not the same, but their intended purpose is arguably the same — giving readers (followers?) a moral framework to function inside (See my answer to “What are morals and morality?”). Generally speaking, all three books (despite the Abrahamic ones being of a distinctly different flavour from the Dharmic one) tell man the way to be. These ways to be are sometimes commandments, as in the case of the Bible and the Koran, and sometimes they are offered pathways that man may choose, like in the Gita. But all three tell man what to do. They presume to know more about humanity than the reader does. Oftentimes, that is the case and the reader does indeed know less. But what must be made clear is that these books are not necessary. Reading them is not an absolute necessity. It is not as if one has to choose one of these options in order to “learn humanity”.
If you are human, and I think you are, then you already know a lot about being human. You are aware of what it feels like. You know what feels good and what creeps you out. You have imagination and reason. You have grown up surrounded by human beings and you have a pretty good idea what that involves. You can tell stories, build machines, navigate your surroundings using your understanding of natural laws. You learnt all this without the Bible, the Koran or the Bhagavad Gita.
And it might come as a surprise to you, but the three books we are talking about were also written by people exactly like you. Well… almost exactly like you. If you ever went to school, I think it is safe to say that they knew a lot less about the universe than you do right now.
Of course, none of this is to say that you know everything and you don’t need to read any of these books. I would say read all of them and then keep going. Don’t stop at any one book and accept all it has to say as absolute. When it comes to “learning humanity”, the simple truth of the matter is that you can only do so if you accept that humanity is a work in progress. It is not what it used to be when these books were written. And it won’t always be what it is right now. So if you ever write a book with the intention of “teaching humanity” to people, know that it too, will not be enough.