While many physical therapists love sports, and are first introduced to the field as injured athletes, it is definitely not necessary to love sports to be a PT. Physical therapy is a field made up of a diverse group of people with a wide range of interests, and there is no one hobby that a PT must have to be successful.
That said, many PT’s are former athletes and tend to be interested in sports. I myself fall into this category since I first became interested in PT after spraining my ankle during cross-country practice. That’s simply how many are introduced to the career, but it doesn’t make or break someone as a PT.
Personally, I think it’s more important to love exercising and working out than to love sports. I feel more reasonable assigning patients therapeutic exercises to do at home when I know that I’ll be doing my own “exercises” that night in the gym. If I’m telling them to workout, it only makes sense that I’m adhering to my own workouts as well. I also make it a goal to at least try every exercise I assign my patients. Many I performed as I learned them in school, but each time my CI assigned a new exercise in the clinic, I made sure to eventually try it out myself. This has lead to me incorporating various aspects of ther-ex into my own gym routine. I can be more empathetic to a patient when I can truthfully admit, “I know side-lying hip abduction is hard; I just did some myself last night.”
Regardless of whether you enjoy sports or working out, from the way you describe yourself wanting to “help people recover and be able to live normally again,” it sounds like you’re going to be a great physical therapist. Good luck with your PT journey!