> Is that not much more 'evil', to breed something specifically to kill it for its skin?
That depends on what value/s you place on the thing being bred for its coat. Pretty much all cultures around the world are different, subtly or dramatically, on such issues.
> If it's not, then why is it not allowed to be done by the same species to itself?
The answer to that is: because the humans judge that the minks (and their existence) are not equals in value to the humans, rather, they're considered property, to be disposed of as the owner sees fit. And obviously that aspect (as the owner sees fit) varies by location/culture.
Your question - then why is it not allowed to be done by the same species to itself? - starts from the incorrect premise that values are objective, such as whether a mink should or should not be considered property (your premise requires starting from the notion that minks have protected rights and are equal to humans generally). Instead, those values are in fact subjective and will vary depending on which culture you're dealing with.