Or, we can take a look at how the recognised authorities do thgings. Here is what the Audobon Society has to say:

There are rules governing the capitalization and hyphenation of birds' names..... It might be helpful to go over a few of the general rules of written bird names. When writing your own name you always capitalize your first and last names, e.g., Sam Spade or Lucy Brown. When writing the English name of a bird species, you should always capitalize its first and last names, e.g., Scarlet Tanager or Winter Wren. This avoids confusion with other modifiers in the sentence. For example, "the secretive, tiny, Black Rail..." If you are referring to unspecified birds use lower case letters, e.g., "those herons over there," or "that sparrow on the ground." If a species has a three-word unhyphenated name, all three words are capitalized. For example, "the graceful American White Pelican..." Many birds have compound or hyphenated "first" or "middle" names. Only the first letter of the compound name is capitalized: Red-throated Loon, or Long-billed Curlew. However, if a bird has a compound "last" name, then both parts of the compound name are capitalized: Eastern Screech-Owl or American Golden-Plover.

Can't get much clearer than that.

If we are to fly in the face of recognised convention in the case of bird and mammal names, why is the so-called "rule" so self-contradictory?

Why are we (according to the name-change people) supposed to use different rules for dogs, and aircraft on the one hand, and birds and mammals on the other?

Tony Wilson (Tannin)