[ Ayabe nods a little, because, yeah. The goal is to be hated, or at least his was. He absolutely does not want to be the center of attention, for good or for bad, and when you're hated you're avoided and that's good enough for him. ]

I don't think it's a pet, though. She just said that they've had troubles trying to build a fence around the lake without it being destroyed. More likely, it's this mansion that was built around the lake.