There is a misperception in many people's minds concerning creativity. It is the belief that a child who looks at the world and can codify it into "drawings" that roughly resemble people or animals is somehow more advanced than the child who refuses to do so.
In my opinion, and in the opinions of many creative people (Leo Buscaglia, for one), being able to draw a green lollipop on a brown stick and call it a tree is actually a stunting of the creative impulse, because it causes the mind to cease seeing things as they are, and breaks down the experience of the world into a series of hieroglyphic images, instead of the 3-dimensional, ever-changing world that becomes more colorful, more meaningful the more one sees. Asking a child to "learn to draw people and animals" in the usual, codified manner may seem to be a step towards art, but in reality, it is a step backwards. It encourages him NOT to see, NOT to be artistic, but to conform to politically correct norms for what does not really exist in nature.
A child who refuses to express himself on paper has, in all probability, been scared away from using paper and pencil by people who have imposed this hieroglyphic vision of the world on a highly creative mind. This type of child, whose mother may say, "We don't expect him to be a great artist; we just want him to know how to draw simple people and animals," may indeed HAVE a great artist on her hands. Most average kids, given art supplies, will be eager to try them all out, and will scratch out hurried and lazy examples of what they think they perceive. Their child won't. Why? Quite possibly because the stick figures, square-and-triangle houses and wavery bobble-headed flowers nearly the size of the house in the picture won't cut it for a child who can plainly see that people are not sticks, his house is not a stacking block, and flowers come in shapes and sizes and colors that boggle the mind. Translating their perception into media is a daunting task, since they actually see the complexity of it all.
So, what can be done for this stubborn creative type who will not draw? First, they must not be over-scheduled and over-stimulated. Children today have so much to do that they have no time to get bored and think the exciting, daring and dangerous thought, "What if?" They have electronic playmates, ready and always willing to play, in living color and with boundless energy, as long as the power supply doesn't run out. There is no need to lift a finger to combat having nothing to do because they are never faced with that. They are everywhere inundated with sight, sound and motion, competing for their attention. They have neither the time nor the need to stop reacting and authentically act.
They must first have a need to find something to do where there is nothing. Then, they must have access to artwork. They must be free to explore their own creativity. Not with expensive art materials that professionals use, but with materials at hand ("So, what can we do with this milk carton? What could this be, if we didn't know it was a milk carton? How can we change it?"). A "seeing child" must be exposed to visual artists' work constantly, and must learn to look at a picture and identify lines, shadows, shapes and colors for what they are. There is no time this child will express their world in any way but from their own gut and experience, unless the creative impulse is completely devalued and crushed within them. This child does best if given the worst, cheapest and least appealing art supplies, because this child is a problem-solver and needs to learn to bring their art out of the mundane.
Anyone can make a pretty hieroglyph, given the proper supplies and a few pointers. But, are they expressing themselves, or becoming a Xerox machine? A "seeing child" will resist this dictate mightily, up to throwing tantrums and exhibiting other forms of misbehavior. Forcing this child to be less than he is by drawing a person by forming a ball here, a stick there, would be like telling a rocket scientist that 2 + 2 = 5 is close enough. It isn't. It is patently wrong, and they know it, and it's going to drive them crazy until you correct the flaw. They need to be around other people who draw, paint and sculpt, so that it seems natural to them to be that way; the way they are intrinsically.
In Native American culture, children are brought up seeing the creativity in all; whether in song, picture, weaving, pottery-making or story-telling. It is taken for granted that people by nature are creative, and their creativity is to be celebrated as a gift to the world. In modern American culture, so much of our communication has been reduced to the hieroglyph, the logo, the icon that all one has to do is see a pair of golden arches, and he gets a hankering for french fries. We have desensitized ourselves to the real, in deference to the expedient. Doing real artwork isn't clean or predictable; it isn't something one can plan to do for an hour and be done. It is something that must well up from within, and then come bursting out onto paper or in clay, or in a myriad of different ways. It is not controllable, but it is manageable. The art itself cannot be taught. The skills in presenting it can be, and its management must be. But, it is not something that can be tamed, because once broken, it is nearly impossible to mend.
My advice for those who have children who "won't draw"? Don't force it. Give them examples of art, give them access to enough free time and odd materials, give them enough "creative neglect" with nothing to do, and then stand back. Once the dam of expectations is gone, and they are bored enough with just sitting, all of a sudden their creativity will assert itself and you will be overwhelmed at the amounts and types of art they will happily come up with.