How are wooden bows so flexible without breaking while the same type of wood used to make a table (for example) would break if you flexed it that far?
There’s a couple of factors to consider.
First, many tables today are not made of a single piece of wood, but several bits of wood grinder up and glued together. If your chunks are woodchip size, this is plywood. If your chunks are smaller, it’s probably some form of MDF (Medium Density Fiberboard). In such woods, the strength of the material will only be as strong as the glue bonding the wood chunks together. Preparing wood this way is adequate for many situations because 1) There is not a lot of force being applied perpendicularly to the plywood/MDF and 2) It’s much cheaper to produce than sourcing real wood (hardwood) in the same dimensions.
Wooden bowls on the other hand are a more of a novelty item, are smaller and do not have nearly the same demand as plywood/MDF. As such, they can be made from hardwood which has the advantage of being much tougher than plywood/MDF (especially if you make your bowl out of oak or walnut).
Secondly, because the bowl is the shape it is, it is much stronger than a flat surface. The curved shape of the bowl allows the bowl to resist deformation much the same way an arch is able to resist collapsing even when it is loaded with weight.
Good bows are made so that they run with the grain of the wood. This gives a lot of flexibility without sacrificing strength, but does waste more wood than cutting planks out if a tree.
Tables are thicker overall, assuming they’re actual wood and not some laminate. They also don’t run with the grain for more cost effectiveness, but you lose flexibility. But who wants a table that bends?
Next is the finish and curing. Tables are dried wood, sometimes they’re treated during the drying. I don’t know what happens to a piece of yew between chopping and shaping, but it’s not going to be the same process.
I don’t know if they make tables out of yew, but the geometry makes a difference. A table is a slab designed not to bend, but to hold up a load. A bow is tapered towards the ends so the flex is distributed in a way the wood can support. Many bows are laminated to increase this ability.