Questions & Answers about Я не умею плавать, поэтому не иду в бассейн.
Because уметь means to know how to do something / to have a learned skill, while мочь means to be able / can in a broader sense.
- Я не умею плавать = I don't know how to swim / I can't swim because I haven't learned
- Я не могу плавать = I can't swim because of some situation, condition, or limitation
So in this sentence, не умею is the natural choice because the reason for not going to the pool is lack of swimming ability, not a temporary obstacle.
After уметь, Russian normally uses the infinitive:
- уметь читать = to know how to read
- уметь готовить = to know how to cook
- уметь плавать = to know how to swim
So Я не умею плавать literally follows the pattern I do not know-how to swim.