Imagine if the sentence said "Du er bedre til svømning end mig." "Svømning" and "mig" seem like they are the indirect objects in the sentence, but that doesn't make sense for the first-person singular. You are comparing two different people's ability to do something, not one person's abilities to do two different things, so both people in the sentence should be subjects. It's really a short form of the full sentence: "Du er bedre til at svømme, end jeg er."
no man I completely understand the rule aha, I use the equivalent of "end jeg" in every other language I speak.
BUT after looking it up it appears that it is the same case with danish. Just figured that it was something like, idk, how in german you say "im August" which is literally "in the August" in english. Just like some sort of a difference from language to language.
but hey who knows, maybe people look at the phrase "end jeg" with even more raised eyebrows than might be done if you say "end mig". I trust the people who made the course picked what's best for a person learning the language informally.
I found a nice quiz about "jeg/mig", including the rules: https://proscript.dk/maanedens-sprogquiz-mig-eller-jeg/