Sometimes, a wood dowel will split lengthwise along the grain when you pound on the end.
And one side of the split will wedge tightly beside the bullet.
Rendering the bullet + wood wedge the Mother of All Bore Obstructions to get out.
It's less likely to happen with a flat-pointed pistol bullet.
But a pointed rifle bullet is almost a sure bet it will end in disaster.
Plus, an old wood rod can hold grit, and is more likely to scratch a bore then a brass or polished steel rod that fits the bore fairly closely.
And the weight of the metal rod alone is usually enough to tap a bullet out without having to hammer on anything.
For that reason, I Never recommend anyone use a wood dowel rod for driving out bullets of any size, shape, or description.
No sense promoting a very bad idea!
rc