Why is Taiwan worried about carriers?

I know that China is refurbishing a carrier and leasing another one, but why on earth would that lead to Taiwan to build an anti-carrier ship? The Diplomat's Jason Miks calls it "interesting". To me, it seems really misplaced.

The greatest threat from China against Taiwan is the vast buildup of missiles facing it, not any Chinese carrier. A carrier does allow China to fly more sorties, or faster sorties at least, against Taiwanese targets. However, China can already fly sorties from the mainland. It doesn't need a carrier to do that. An anti-carrier boat is nice, but not essential to Taiwan's defense. Taking down those missiles (or some good portion)? Much more essential.

So, because I refuse to believe that groups like this never do anything for blatantly illogical purposes, what's the point? What's going on? Is it just balancing against a new threat (while ignoring the bigger, present one), or is there a hidden strategy at work?