@Laura2811 You should definitely disclose the existence of the rooster in your listing, which is quite a bit different than just saying there are chickens, which only make some little clucking noises, not something that would wake people up. And provide earplugs for your guests.
That said, guests booking a place and then even thinking about reporting a neighbor, who I imagine has been living there with his chickens and roosters for quite awhile, is outrageously entitled behvior. If they don't like it, they should leave.
I agree with Mark, tell these guests that it's unfortunate, but it doesn't seem that your place is suitable for them and try to get them to go. Be prepared to not get paid for remaining days, and they may even get a full refund from Airbnb- they are pretty obviously the kind of people who are going to demand one, but its better than them creating bad blood with your neighbor.