Learn English – the figure of speech called when there is a conjunction of things that are actually in subset relation

I spent a little time researching the various figures of speech and found a few that are certainly related to the form you are describing. The specific pattern you note wasn't on Wikipedia's list (or I missed it) but the general purpose of the form is probably covered by a mix of the following terms.

polysyndeton — the use of several conjunctions in close succession, especially where some could otherwise be omitted (as in "he ran and jumped and laughed for joy").

Your example is using explicit repetition of similar terms in order to achieve a particular effect. This is more explicitly evoked when the list is greater than two:

I love cats and mammals and animals!

And it can be used in "reverse":

I love animals and mammals and cats!

It does not, however, cover the intended comparisons which is mostly evidenced by this counterexample:

I love animals! Well, mostly mammals. Okay, cats. I love cats.

The de-escalation close enough to your example that I would want to classify it as the same figure of speech and, therefore, "polysyndeton" is not a complete match.

pleonasm — the use of more words or parts of words than is necessary for clear expression: examples are black darkness, or burning fire. Such redundancy is, by traditional rhetorical criteria, a manifestation of tautology.

Pleonasm applies to the redundant, tautological aspect of your example:

I love animals and cats!

If you scan through the myriad of examples on Wikipedia, you can notice that redundancy is the key aspect of classifying something as a pleonasm. A few handpicked examples:

• This was the most unkindest cut of all.
• Receive a free gift with every purchase.
• Please R.S.V.P.

The redundant use of "cat" after using "animal" matches the strict definition of a pleonasm but since the redundancy only travels one way, I do not think the pattern is a perfect fit.

climax (figure of speech) — a figure of speech in which words, phrases, or clauses are arranged in order of increasing importance.

• "There are three things that will endure: faith, hope, and love. But the greatest of these is love." 1 Corinthians 13:13
• "...Lost, vaded, broken, dead within an hour." William Shakespeare, The Passionate Pilgrim, XIII

If your usage always traveled from "subcategory" to "supercategory" you are operating with a climax. The emphasis of performing this pattern is consistent with the purpose of using a climax and, therefore, your form qualifies.

Reversing the order actually shows how the climax works:

1. I love cats and mammals and all animals!

2. I love animals and mammals and cats!

Due to how climaxes work, the most important variant is the one listed at the end. If you wanted to convey that you love all animals, (1) is the best choice. If you, on the other hand, you wanted to convey a special love of cats you should use (2).

hendiadys — a figure of speech used for emphasis — "The substitution of a conjunction for a subordination". The basic idea is to use two words linked by the conjunction "and" instead of the one modifying the other.

• "the cold and the wind went down the hall" instead of "the cold wind went down the hall"
• "He came despite the rain and weather" instead of "He came despite the rainy weather".
• "ruined and broken", but the phrase means "totally destroyed"

A hendiadys matches the unnecessary repetition and also allows for a drastic scaling difference between the two words. The choice of splitting the description of "animals" into "cats and animals" fits the description of hendiadys in the sense that you are using two (or more) terms instead of one. The extra term is purely for rhetorical effect.

The only problem with classifying your form as a hendiadys is that the other examples are pointing toward splitting one term into two terms. "Cold wind" becomes "cold and wind"; "rainy weather" becomes "rain and weather". Taking "cats" out of "animals" and then including it is slightly different.

In the end, these were the four terms I found most similar. Two of these terms apply due to the specific form (polysyndeton and hendiadys) while two apply to the particular emphasis or effect (pleonasm and climax). To accurately describe the form I would, therefore, use something along the lines of "climactic polysyndeton" to describe the form used in "I love cats and mammals and animals!"

If you are merely aiming for an emphasis of redundancy, it could more accurately be termed a "pleonastic hendiadys". This would more accurate match the form of "I care for the plants and flowers."

Aside from these terms, you are on your own. The form is distinct enough from those I've listed here that I think it is a suitable target for a neologism but creating one is outside of the scope for this site.