J.A.
Hi Juliana,
It depends on how you consider swimming. If it were a particular sport or playing an instrument etc. that he didn't want to do, I would say clearly the interest is not there and you'd be better off trying something different. Even if it were simply a matter of excercise you could just choose a different activity.
Swimming, however, is a necessary life skill that could someday save his life. If you are serious about him learning to swim I would hold my ground on this one. You could ask him if he has a specific complaint. (he doesn't like the teacher, the water is too cold etc.) you could work with that but otherwise, no negotiations. If you cave on this you will be caving on everything.
If he has a true phobia of the water, share this with the instructor. They have specific policies as to how to handle this situation.
Press him for a reason as to why he doesn't want to swim. "Just because" is NOT an answer.
Best Wishes,
J.