Actually, I thought plastic in a microwave emits dioxin. Had not heard of paper or cardboard.

Do they still use chlorine bleaching processes on tree pulp these days?
dioxin is a bi-product of industrial (high temp and pressure) chlorine bleaching processes
(I think peroxide processes are more common now, but maybe some holdouts)

Dioxins are released during combustion so when the paper is hot enough to be on fire