It bends away from the bow because the bow is in the way the other direction.
No. It is because of finger release and momentum of arrow point, i.e. buckling.
Try to shoot so that there is 5–10 millimeters gap (air) between bow riser and arrow. There will be no contact or interaction between the bow and arrow. You will get quite good arrow flight with different kind of arrows. In fact, that technique could work nice in flight shooting.
Why doesn't the arrow bend up? What happens with a centershot bow? The same forces are in effect, aren't they?
Because there are no vertical forces. The arrow bends always to direction of fingers tips, that is for example difference between mediterranean release and thumb release. With pure centershot bow with release aid the arrow is bending because of buckling but you can not predict the bending direction if net force is zero. The cleaner release (less movement), the better arrow flight, usually. That is why release aids are so good.