The thing with analysing any piece of satire is that there is a fundamental question as to what parts are satirical, and what parts are played straight. As such, the argument can cut either way. Ian Bradley, in The Complete Annotated Gilbert and Sullivan, regards 'He is an Englishman' as a straightforwardly flag-waving piece, whereas James Brooks Kuykendall, in The Cambridge Companion to Gilbert and Sullivan, refers to the lyrics as merely 'quasi-patriotic'.

Kuykendall doesn't go deep into the lyrics as his focus is on the music, but one thing he does bring up is worth bearing in mind:

Gilbert’s lyrics are satirical, but Sullivan fits the Boatswain’s sincere expression to a tune which seems always to have sounded somehow familiar.

Gilbert and Sullivan were not always in perfect accord in terms of their artistic intentions, and their partnership also functioned in such a way that after Gilbert wrote the libretto to a show, he generally let Sullivan do what he wanted with the music, to the point where he readily altered his lyrics to suit the music if needed. It is often said that Gilbert had significant musical input on all of one number during his 14-opera partnership with Sullivan, that being the folksy 'I Have a Song to Sing, O!' in The Yeomen of the Guard, where Sullivan wrote the melody based mainly on an improvisation by Gilbert.

This in turn has implications for why we might discern a certain dissonance between Gilbert's intentions and the eventual impression created by the song as performed. Gilbert certainly accepted far more of the conceits of Victorian society than we would, but he remained a satirist, and his purpose was to criticise, not to laud, his subject matter. Sullivan, however, was far more overtly nationalistic in his tastes: he would later go on to score Julian Sturgis' grand opera adaptation of Walter Scott's Ivanhoe, a piece infused with its source material's 'Anglo-Saxon' nationalism, and which – were it not for its relatively modest success – was intended as a springboard for what was hoped would be an English – and, given Ivanhoe's subject matter, very specifically English – tradition of grand opera to rival its continental counterparts. Indeed, the tune to 'He is an Englishman' would later be resurrected for Queen Victoria's Diamond Jubilee in in 1897, for which Sullivan composed the music to Victoria and Merrie England: A Grand Ballet in Eight Tableaux. In the final scene, '1897 – Britain's Glory', after a parade of dancers in the dress of the regular Army, the tune is then used for the entry of the Volunteers. Without being too insulting to Sir Arthur, it ought to be said that he could well have missed the joke.

And there is, in fact, a joke, because the straightforwardly nationalistic interpretation of 'He is an Englishman' is one that works because it is often divorced from its original context within the opera it was written for. For that, we need to briefly summarise the relevant plot details of H.M.S. Pinafore and give the immediate context:

Ralph Rackstraw is an Able Seaman aboard HMS Pinafore, who is in love with Josephine, the daughter of presumed widower Captain Corcoran; unbeknownst to him, she is in love with him as well. Captain Corcoran, however, is attempting to get Josephine to marry Sir Joseph Porter, the First Lord of the Admiralty, a self-made man of ostensibly egalitarian principles who would be willing to marry a woman below his station, because 'love levels all ranks'. Ironically emboldened by Sir Joseph's radical ideas, Ralph and Josephine confess their love and plan to elope ashore, helped by several of the crew, but the captain is tipped off about this and intercepts them before they are able to escape, singing (with what I believe is one of Gilbert's most fun rhymes near the end):

Pretty daughter of mine,
I insist upon knowing
Where you may be going
With these sons of the brine.
For my excellent crew,
Though foes they could thump any,
Are scarcely fit company,
My daughter, for you.

Ralph and Josephine declare their love before the captain, with Ralph singing:

Proud officer, that haughty lip uncurl!
Vain man, suppress that supercilious sneer,
For I have dared to love your matchless girl,
A fact well known to all my messmates here!

I, humble, poor, and lowly born,
The meanest in the port division
The butt of epauletted scorn
The mark of quarter-deck derision
Have dared to raise my wormy eyes
Above the dust to which you'd mould me,
In manhood's glorious pride to rise,
I am an Englishman, behold me!

It is after this that the Boatswain steps in to sing 'He is an Englishman':

He is an Englishman!
For he himself has said it,
And it's greatly to his credit,
That he is an Englishman!

For he might have been a Roosian,
A French, or Turk, or Proosian,
Or perhaps Itali-an!

But in spite of all temptations
To belong to other nations,
He remains an Englishman!
He remains an Englishman!

In response, the Captain sings:

In uttering a reprobation
To any British tar,
I try to speak with moderation,
But you have gone too far.
I'm very sorry to disparage
A humble foremast lad,
But to seek your captain's child in marriage,
Why, damme, it's too bad!

In the end, a side character, Little Buttercup, reveals that she had been a baby farmer who accidentally swapped Ralph and Captain Corcoran as infants, and that by some legal loophole, Corcoran is in fact an Able Seaman while Ralph is the captain of HMS Pinafore. Sir Joseph chooses to call off the engagement to Josephine, as, when reminded of his statement that 'love levels all ranks', he replies:

It does to a considerable extent, but it does not level them as much as that.

And Ralph and Josephine are able to get married after all, ex-Captain Corcoran marries Little Buttercup, and Sir Joseph marries his cousin, end of show.

What you will note in all of that is that Ralph's nationality is never in question. The critical conflict of the story is a love triangle between three people of differing class: the working-class Ralph Rackstraw and the upper-middle-class, nouveau riche Sir Joseph Porter vying for the affections of the lower-middle-class Josephine Corcoran. During the sequence of songs from 'Carefully on Tiptoe Stealing' through to 'My Pain and My Distress' (though in the score itself, the whole thing is a single number, which some performers refer to collectively as 'The Plot Song'), what Ralph and Corcoran have mainly sung about relates to that class divide:

• Corcoran brings up that the crew, whom he refers to as 'sons of the brine' in a pretty direct reference to their largely labouring status, are 'scarcely fit company' for Josephine, a point that is hit home when the crew repeat Corcoran's last four lines, but with a change to (italics mine) 'we're scarcely fit company | for a lady like you'.

• Ralph alludes to being looked down upon by his superiors in the Navy hierarchy, calling himself 'The butt of epauletted scorn | The mark of quarter-deck derision'.

• After 'He is an Englishman', the Captain again goes back to the issues of class and hierarchy, with his point being that it is inappropriate, indeed impossible, for an enlisted sailor to seek to marry a captain's daughter.

Ralph bringing up his Englishness is thus fundamentally irrelevant to the matter at hand. Nobody doubts he is English, and whether he is English or not has no bearing on the matter of his status in society relative to Josephine, which is the core source of conflict. The Boatswain suddenly stepping in to lead the ship's crew in a rousing affirmation of Ralph's Englishness does nothing to actually resolve the issue. Indeed, it is immediately followed by the Captain returning to the plot-relevant matter, with the subtle and perhaps intentional detail that he refers to Ralph as a British tar and not an English one. In other words, the entire song is a Big-Lipped Alligator Moment that will have no bearing on the plot going forward.

And, if we look at the lyrics themselves, it is hardly a particularly insightful statement about the nature and importance of Ralph's identity. All that the Boatswain really says, to put the whole thing in summarised plain English, is that:

1. Ralph is an Englishman; because
2. He says he is; which is great because
3. He is indeed an Englishman; because
4. There are other nationalities he could identify as; but
5. He doesn't.

But... so what? The Boatswain doesn't say, and the Captain immediately returns to the point at hand.

An interesting point highlighted by Carolyn Williams in Gilbert and Sullivan: Gender, Genre, Parody is that the Boatswain's suggestion that nationhood would be based on self-identification, that Ralph chooses to declare himself an Englishman and not a different nationality, would be considered pretty ridiculous to a Victorian British audience that would have seen national identities as decided by one's birth. The Boatswain's song thus becomes even more pointless by making a – to the Victorians – nonsensical argument to affirm Ralph's Englishness even more than it can actually be demonstrated.