It's unbelievable how intuitive animals can be. I used to have a red heeler that I used as a therapy dog - I would take her to nursing homes and the chemo clinic. She loved everybody and would go right up to most people. There was one lady she skipped over at the chemo clinic, and I found out later that person was afraid of dogs. Penny (the dog) sensed that fear and didn't approach her at all.

Katie, my current cat, is very tuned in to emotional upsets. If I'm having an argument with DH, she will sit right at my feet and meow loudly, make eye contact with us, try to jump into my arms, wash my face if I hold her..... it's like she's trying to let me know she's on my side.