The broad-backed hippopotamus
Rests on his belly in the mud;
Although he seems so firm to us
He is merely flesh and blood.
Flesh-and-blood is weak and frail,
Susceptible to nervous shock;
While the True Church can never fail
For it is based upon a rock.
The hippo's feeble steps may err
In compassing material ends,
While the True Church need never stir
To gather in its dividends.
The 'potamus can never reach
The mango on the mango-tree;
But fruits of pomegranate and peach
Refresh the Church from over sea.
Of this Davidson says:
Here we are neither told that the Church resembles a hippopotamus (as in simile) nor bullied into making this comparison (as in metaphor), but there can be no doubt the words are being used to direct our attention to similarities between the two.
And so we might leave it if we had no reading skills; but, however rudimentary they may be, we do, and so we won't. And what we find when we actually read the poem is that it is simply false to say that "the words are being used to direct our attention to similarities between the two". On the contrary, the repeated result of comparison in each case is to draw attention to differences between the hippopotamus and the Church (at least in its own self-image). The hippo resting on the mud seems firm, but is really just nervous flesh and blood; the Church resting on a rock can never fail. And so forth. And the contrast is maintained throughout the poem, even in the stanzas Davidson doesn't quote, where the joke of the poem, which is satirical, is completed by the hippopotamus going to heaven while the Church remains mired on earth. It's essential to the joke, in fact. The contrast superficially seems to favor the Church, but a closer look shows that the features attributed to the Church, which seem at first glance to indicate its superiority, are rather odd, as with the "need never stir" or even "it is based upon a rock," with its ambiguity between 'founded upon' (the expected meaning) and 'copied on the model of' (which fits the rest of the poem). They become odder:
At mating time the hippo's voice
Betrays inflexions hoarse and odd,
But every week we hear rejoice
The Church, at being one with God.
The hippopotamus's day
Is passed in sleep; at night he hunts;
God works in a mysterious way --
The Church can sleep and feed at once.
Somnambulant grazing is not what one normally thinks of as a Note of the True Church; and what makes the joke in the first part of the poem is this pompous, hypocritical eulogizing of greedy laziness.
Davidson makes a very odd comment immediately after the one quoted above:
Nor should there be much inclination, in this case, to posit figurative meanings, for in what words or sentences would we lodge them? The hippopotamus really does rest on his belly in the mud; the True Church, the poem says literally, never can fail.
This is one of those sentences with which you suddenly feel you must have missed something. The hippo may rest his belly in the mud; but the True Church "never can fail / For it is based upon a rock" and that latter seems very much to suggest a 'figurative meaning', or, at least, would to someone who (unlike Davidson) thinks there are figurative meanings. Moreover, given the heavy irony lacing the poem, it's doubtful that there's any part of the poem where the believer in figurative meanings couldn't say that there's reason to attribute figurative meanings to it.
In any case, to get back to the original point, the poem, despite making use of an explicit comparison between the hippo and the Church, doesn't suggest similarities between the hippopotamus and the Church because it suggests only dissimilarities; even the verbal echoes in each description are purely verbal. It is being used to direct our attention not to how the two are alike, but to how the two are different (with the Church superficially, but the hippo really, getting the better of the contrast). The Church is not like a hippopotamus; would that it were, since as it is, it is merely the Church of Laodicea.
