Bears will rip that apart, but frankly it is not realistic to think you can build a bearproof coop (except in the sense of using a very well-charged electric fence to keep them entirely *away from* it) so I do not see a lot of point in worrying about THAT aspect.
My uncle has had a large raccoon rip apart 3/8" plywood - it was not brand new but it was not in terrible shape either. I would guesstimate that 1/2" would be reasonably safe, as long as there are not loose edges/corners where an animal can get a grip to pry. (And if it *can*, you are best off having it attached with screws not nails, a goodly number of them, into stout thick wood not just little 1x stuff)
Of course rats will gnaw through pretty much anything nonmetal, but they will not generally do that in areas that are pretty exposed. UNDER a low coop, yes; on the siding, generally no.
JMHO, good luck, have fun,
Pat