Almost everyone I know wanted to be a veterinarian at one point in their younger years. Either their grades in school or finances kept them from becoming one. There are many other animal health careers besides vets. There are veterinarian technicians, lab technicians, horse dentists and artificial insemination technicians. Those are just a few animal health careers.
Those people that have tried to go from human health careers to animal health will find that their nursing or medical assisting certification will do little to qualify them for a career with animals. The training and biology is totally different.
Those that do pursue a career with animals in their health care will have a large variety of locations and types of animals to work with. Large dairies, zoos, racetracks as will as the local animal shelter all need and hire animal health technicians.