The short version
A tight barrel has to hold liquid for years without leaking and contribute flavour while doing it. Only white oak does both, because structures called tyloses block its pores - red oak, which looks similar and costs less, leaks.
Stage by stage
White oak stand
Grown slowly for tight rings, in the eastern United States or central France. Age matters: a stave log may be well over a century old.
Stave bolts
Only straight, clear sections qualify. Most of the tree goes to flooring, joinery or firewood instead.
Note: A large majority of the tree never becomes staves.
Splitting and seasoning
Staves are split or quarter-sawn so the grain runs the length of the piece, then air-seasoned outdoors for months to years, which leaches harsh tannins before the wood is ever bent.
Note: Seasoning losses and rejects are substantial.
Raising and toasting
The cooper raises the staves into a cylinder, draws them together with hoops, and toasts or chars the inside over fire. The degree of toast is a flavour specification the buyer orders by name.
Tight barrel
Sold individually, by origin of oak, grain tightness, seasoning time and toast level - a specification sheet, not a commodity.
Wine and spirits
Bought as a production input that is also a flavour ingredient, and resold second-hand down a chain of other drinks industries once its first use is done.