A true example: A couple of years ago, my toddler son was in the Emergency Room for croup, a severe breathing issue for an asthmatic child. His nurse, who had not been paying the attention that was required, provided him with an adult dose of the wrong medication! Thankfully, he was okay, however delayed 8 hours for monitoring in the hospital. The outcome could have been, but wasn't, life threatening.
Take control of what you are doing. Make sure that with responsibility comes the attention to detail required to care for the life of another. The same is true if you choose to care for an animal when their owner is not home. To you, it may be just a dog or cat, but to the family, it is a loved one and as much a family member as anyone else.
If you choose not to do so and get fired, it is nobody's fault but your own, and that is a rough one to explain away in an interview!