By way of illustration, think of a half pipe shape where the back of the bow is concave and the belly convex. Bending that bow tends to widen the C section. The same thing happens, to a lesser degree, if the back of the bow is flat and the belly convex.
Millions of bows have been made and used that have that cross-section. But if the wood is easy to split and the physical limits are exceeded, the chance of your result becomes less unlikely.