I recently built the cartographer's guild, and then I noticed some problems.

The first being that there are two pets in the same place. I'm pretty sure they're supposed to chase each other off.

The second being that blank space next to the Dragon.

The third one may be a glitch, or it may also be intentional. It's not allowing me to place a Bird Catcher or Magic Catcher on the eastern fields. I think this one may be intentional because, going by the FAQ, that Griffin is going to head to a hunting area next, and I've placed bird catchers on the other two hunting areas with the eastern fields being the third. I think this might be intentional to prevent people from always getting the pet that they're aiming for.

The Big Field and the Waterfall have 2 places. In your case the pets do not fight on the Big Field because there's enough space for both of them, and the second place on the Watefall is free at this cycle.

You don't have any free Bird or Magic Catchers so you can't place them anywhere.