It's trivial to drill gently curved holes in wood using a Forstner bit or a suitably shaped spade bit. You can cut the workpiece in half, rout or mill a curved channel in both halves and fasten the two halves back together. You can use a curved electrode with electrochemical or electrical discharge machining. Of course, the best option is to design the part without a curved hole in the first place.

Electrical discharge machining, seriously? Not even well equipped machine shops are likely to have such specialized equipment.

I think you're proving his point that subtractive fabrication technologies have their limits (as do additive).

https://en.wikipedia.org/wiki/End_mill ?