The air will essentially suck out some of the moisture of the cookies and bread to equilibrate somewhat over time–meaning they go stale. Bread has a lot of surface area, so the moisture gets pulled out of that first, and it equilibrates much faster *without* pulling moisture out of the cookies nearly so much.
The bread has more moisture than the cookies do. Bread that is as moist as a cookie feels dried out because it usually has more. Cookies with as much moisture as bread tend to crumble and fall apart.
Stick the bread in the cookie jar and the moisture in the bread helps keep the moisture level in the jar higher than what is needed for the cookies to be moist, but it’s still drying out compared to the typical moisture level of the bread.
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