I think what you're saying is that cats are an invasive species *because* they kill so many birds. If that's the case, then, "Cats kill an insane number of birds." is a support for "They're very much an invasive species." rather than an additional thing that must be true to make the challenge work. However, while saying that they're an invasive species is a persuasive way of thinking about the subject, it might be a weak link as part of a challenge, because it is harder to consider whether it is true or false. If the concern is whether people care about cats killing a lot of birds, then it might make more sense to write it more directly in this case, such as, "Having a healthy local bird population is better than having a cute pet." It then complements the second statement rather than overlapping with it. Also, it might be better to edit the second statement down to, "Cats threaten the local bird population.", because deciding whether or not it is selfish to own them doesn't change the effect that they have, but at the same time it's a hard accusation to ignore, which means it is likely to derail the discussion. I think the new version of the two statements would make a good challenge because it requires some thinking to consider how cats could be better than dogs if both those things are true, and the fact that they are very straightforward makes it easier to discuss whether they're true (and probably harder to argue that they are false).
The statement above does not appear in any challenges, supports, or specifications of other statements.