I was reading Kollár and Mori's book today and stumbled on the following passage:

"The $\mathbb{Q}$-factoriality assumption is a very natural one if we start with smooth varieties, and it makes many proofs easier. On the other hand it is a rather unstable condition in general. It is not local in the Euclidean (or étale) topology, and it is very hard to keep track of when we pass from a variety to a divisor in an inductive proof."

(For those curious this is in section 3.7)

My question is, what are some examples that show why $\mathbb{Q}$-factoriality is not local in the étale topology?