Then you have to argue that professional athletics isn't a job either, then you'll have to explain why and also explain what makes something a job
If you are going to argue that a student playing sports is a job, then that applies to all sports at all schools, including high school.
College sports are secondary to academics, same as in secondary school. Students are there first for an education, sports 2nd. Are some players only college to play ball? Sure, but they are still getting the education, they still attend classes and need to pass courses. Most colleges are public and are funded through state tax dollars.
Professionally sports players are not in school earning an education for where they play. They are funded by corporations and private owners. Loopholes allow state taxes to pay for crap like stadiums and such, but they don't pay player salaries. Pro players have contracts, agents, unions. etc.
I'm not sure why this needs to be argued. Yes you can compare one to the other because they both play the same game, yes both make money for organizations, but that does mean they are equal. Pro ball players can get long term contracts and could play up to a decade or more. A college athlete at most gets 3 years and 4 if they are good enough. Many don't make it past the college level.
And if you really want to get down to my opinion. I don't consider pro sports a job. It's only for the special elite that get lucky enough to continue to play sports for money. It's short term for most.
