Talk about your affinity for animals. As a vet assistant, you an animal lover experienced with pet sitting and caring for your own pets. Your relationship to the animals in your life tells a vet that you are compassionate. Think about setting up your example like this:

"I adopted my dog from the shelter. He was a rescue with severe anxiety. I spent the first six months training him and spending time to build a bond with him. Even though he had some bad behaviors, like peeing on the floor and destroying the house when I was gone, I learned that time and patience paid off. He is an awesome dog and I am so grateful to have him in my life."

Telling a brief story about a relationship with your pet is a great way to respond to this question. You could also talk about an animal you took care of for someone else. Talk about what you learned from the experience.