We become so attached to our pets, that we can't imagine giving them up. Most people that are allergic to animals are also allergic to pollen and dust particles in the air and outside.
I know that getting allergy shots have been successful for many people who have not wanted to give up their pets. They also found that this helped them with their allergies over all, so they even felt better.
This would be a winning combination for me - feeling better and being able to keep my pet at the same time.