Why use "at svomme" when kan is a modal verb?
Because 'kan' here indicates the modality of "lide", not "svømme". The cat can swim, but it does not like to do so.
Thanks so much!
What's the difference between "kan lide" and "kan godt lide"?
Nothing except that "kan godt lide" is more commonly heard.
"Kan godt lide" is just what they do. There's no real reason beyond that. In my head, however, it seems as though by saying "godt" you would sound more sincere (at least in the positive sense of liking, as opposed to "disliking").
You’d be surprised!