If explained within the framework of Tinbergen's four questions: (don't take it much seriously)
The proximate explanation is, because it's a convention in the biological society. In academic field, every creature's name is written in katakana when it refers to a equivalent of a scientific name. It once was even required by law (though it didn't state explicitly to use katakana). Today, the practice is getting more and more popular, which I think because we do it extensively in the science class, that even people unrelated to biology prefer katakana for any plant or animal name.
The ultimate explanation is, it stands out in text. The original intention why biologists started to write them in kana, I guess, was they wanted to distinguish them from ordinary words, while Japanese writing doesn't have italics or Capital Letters. Interestingly, in the pre-WWII ages the academic documents were commonly written in mixture of kanji and katakana, so they used hiragana to render those terms. Nowadays we use hiragana for standard orthography, and katakana for foreign words. Since many plants and animals are innately written in katakana, it may be felt consistent to write all of them in the same way.
Note that not every situation is appropriate for katakana. Vegetables, meats and fishes in the store (as well as woods) are less likely to written in katakana. Generic words (fish, bird, mammal, or bear when you're talking about many bear species) are often left in hiragana or kanji. Advertisements prefer kanji, especially when they want it looks classy.