Actually I was once chased by a cat
Back when I lived near Seattle I used to go ride around Lake Washington, or other times I'd cut across Mercer Island and ride my way over to the Shilshole marina. One day I did the Shilshole ride, went north past the Marina, then cranked up the hill and into the residential area. I was riding down a street and saw this big housecat sitting on a porch watching me. As I got closer the cat got into a pounce posture and started lifting it rear end like it was going to jump off the porch. I figured it was just going to jump into the bushes and hide as I rode past. But no, not this cat, this cat pounced off the porch, raced across it's front yard just as I got in front of it's house, looped past me on the sidewalk, then arced into it's driveway as I got to the edge of it's "zone of protection". So, yep, I've been chased by a cat while riding my bike.
I've also been bapped in the head several times by an owl while riding in Souhtern California.
Bicycling, you just never know what might happen next.