"Desinat in piscem" in Horace's Ars Poetica: morphology or looks or what exactly?

Question

This is about the core meaning of desinat in piscem as in:

Humano capiti ceruicem pictor equinam
iungere si uelit et uarias inducere plumas
undique collatis membris, ut turpiter atrum
desinat in piscem mulier formosa superne,
spectatum admissi, risum teneatis, amici?

[Quintus Horatius Flaccus (Horace), The Art of Poetry: an Epistle to the Pisos]

Of course I understand desino/ere is a transitive verb meaning to end (in) and there's the preposition in and the accusative piscem, literally (I'm guessing) end in fish.¹ I would describe the image the author crafts as an example of a type mismatch of sorts but this is not the point. The Gaffiot Dictionary also refers to Virg. En 10, 211; Sen. Ep. 92, 10; 66, 43 for the expression.

As far as fish are concerned, they don't necessarily strike as beautiful-looking creatures (but then again it's all a matter of perspective). There's also morphology, which might vary depending on where one lives, and often the fish is wider in the middle and ends with a smaller section before the tail, so there's a contrasting element. Otherwise I'm not clear on the eating habits of the classical authors (and it's off topic) but more importantly I'm not clear on the references they might have about fish and how this translates into Latin, into this desinat in piscem.

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• In Horace's, Seneca's, and Virgil's Latin, does desinat in piscem refer to the end/tail/shape of the fish, or rather its looks ? Is that some figurative use for some bad omen or a non sequitur, or just plain bad taste or what exactly? How and why are they using this?
• Is there more to be said about the use/analysis of in piscem generally, or with other verbs; anything peculiar I should know about the construction in + animal name (acc.), is that a significant construction in Latin; does that provide further insight about Horace's quote and if so, how?

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_{¹ It is said (DHLF/Rey) that in French, finir en queue de poisson (lit. to end as/like the tail of the fish) coined by Honoré de Balzac (1833) is inspired by Horace's desinat in piscem; some French translations of Horace's text even refer to the fish tail per se. It goes without saying that the sentence desinat in piscem doesn't contain the word tail; but that doesn't really mean anything.}

Answer 1

Horatius describes a "combined animal" with human's head, horse's neck, bird's feathers and fish's rear end. This creature ends in a fish: instead of legs it presumably has a fishtail. No details of the fish are given; just that the creature contains a fish-like part.

The translation available at Perseus (the Latin version is there, too) puts it like this:

If a painter should wish to unite a horse's neck to a human head, and spread a variety of plumage over limbs taken from every part, so that what is a beautiful woman in the upper part terminates unsightly in an ugly fish below; could you, my friends, refrain from laughter, were you admitted to such a sight?
(Horace. The Works of Horace. C. Smart. Theodore Alois Buckley. New York. Harper & Brothers. 1863.)