Why are Catholic bishops styled as archbishops?

I going to try and explain why Catholic archbishops and bishops are addressed as "Most Reverend".

First of all there will invariably be some local tradition that will differ as to how the faithful address archbishops and bishops.

Generally speaking most archbishops in the Catholic Church are Metropolitan Archbishops, but there are some archbishops that are Non-metropolitan Archbishops.

Archbishops

The title of archbishop is held not only by bishops who head metropolitan sees, but also by those who head archdioceses that are not metropolitan sees (most of these are in Europe and the Levant). In addition, it is held by certain other bishops, referred to as "Titular Archbishops" (see "Other Bishops" below) who have been given no longer residential archdioceses as their titular sees—many of these in administrative or diplomatic posts, for instance as papal nuncios or secretaries of curial congregations. The bishop of a non-archiepiscopal see may be given the personal title of archbishop without also elevating his see (such a bishop is known as an archbishop ad personam), though this practice has seen significantly reduced usage since the Second Vatican Council.

There even exists a few archdioceses that do not form part of any ecclesiastical province. The Roman Catholic Archdiocese of Monaco is an example of this.

The Roman Catholic Archdiocese of Monaco (Latin: Archidioecesis Monoecensis) is an exempt Latin ecclesiastical territory or archdiocese of the Roman Catholic Church in Monaco, directly subject to the Holy See, not part of any ecclesiastical province.

Since most archbishops are metropolitan archbishops, but not all, it seems that the address of "Most Reverend" in the Catholic world became the norm for all bishops regardless if title of archbishop has been conferred on them by right or by privilege.

In the Archdiocese of Vancouver (Canada), Archbishop Miller enjoyed the title of Coadjutor Archbishop of Vancouver before even being the Archbishop of Vancouver. Thus we see that some archbishops are really bishops that have been given this title, but really rank as ordinary bishops.

When I was in the seminary, we were taught that monsignors, abbots and major superiors of religious orders were to be addressed as Right Reverend.

More information can be read here: Ecclesiastical Addresses

In the Anglican Communion, archbishops are styled "The Most Reverend" and addressed as "Your Grace", while bishops are styled "The Right Reverend" and addressed as "My Lord" or "Your Lordship". (In some countries, this usage is followed also by the Roman Catholic Church, but in others no distinction is made and "The Most Reverend" and "Your Excellency" are used for archbishops and bishops alike.) Anglican archbishops are entitled to be preceded by a server carrying an archiepiscopal processional cross (with two bars instead of one) in liturgical processions. - Archbishop (Wikipedia)

Contrary to the premise of the question, not all Catholic bishops in the British Isles are Right Reverend. Since the 1860s all Catholic Bishops in Ireland have been Most Reverend. In England, Wales and Scotland Most Reverend is reserved for archbishops and Right Reverend for bishops. This Most/Right distinction is also used in the Church of England and Church of Ireland, except that the Protestant Bishop of Meath and Kildare is a Most Reverend.

The distinction is mirrored in the secular peerage. In the English Order of Precedence, C of E archbishops rank below Princes but above non-Royal Dukes, while bishops are between viscounts and barons. Dukes are Most Noble while Viscounts are Right Honourable; so it is perhaps appropriate that archbishops use the same grammatical intensifier, Most, as dukes, and bishops use the same grammatical intensifier, Right as Viscounts.

Erasmus (1466 - 1536) wrote numerous letters which were collected, numbered and published. In May 1519 he wrote letters to the Most Reverend Archbishop of York (letter 967) and to the Right Reverend Bishop of Durham (letter 974) which shows the distinction was made before the Reformation reached England.

After the Reformation the Irish sees continued as before both in the Church of Ireland and in the Roman Catholic Church. So there were two bishops of Derry, one Protestant and one Catholic; and two Archbishops of Armagh, one Protestant and one Catholic. Though there were gaps, and later amalgamations especially in the C of I. The honorific Most or Right Reverend, pertaining by law to the Protestant clergy, was used also for the Catholic clergy within the Catholic community and often, by courtesy, outside it.

In England the Roman Catholic succession to episcopal sees died out. From 1685 to 1850 England's Catholics were served by Apostolic Vicars of which there were 4; for London, Western, Midland and Northern regions; increased to 8 in 1840. These Apostolic Vicars were in fact bishops, but not of anywhere in England. They held titular sees in Islamic countries which had once had resident bishops, but where there were no longer any bishops, or even any Christians.

In 1850 a new Roman Catholic hierarchy was erected in England. It did not replicate the Church of England: there was no Catholic Archbishop of Canterbury to rival his Protestant counterpart. Instead there was an Archbishop of Westminster and twelve Catholic bishops, all of towns which had no Protestant Bishops; but including Bishop of Liverpool and Bishop of Birmingham, two of England's greatest cities. These had, as yet, no Protestant bishops, as they were part of dioceses centred on the ancient, but now much smaller, cities of Chester and Worcester.

This had not been expected to be particularly controversial, but it was. Politicians and Protestant Churchmen, Anglicans, right across the spectrum, and Dissenters alike, were outraged and vehemently denounced the Papal Aggression as it was called. Parliament passed emergency laws forbidding the use of such titles anywhere in the UK (including Ireland where they had been used for centuries). There were widespread riots and attacks on Catholic property. Effigies of Cardinal Wiseman and Pius IX joined those of Guy Fawkes and Paul V on Bonfire Night. Even Queen Victoria demanded angrily to know "Am I Queen of England, or am I not?"

The Ecclesiastical Titles Act was largely ineffectual. It was studiously complied with by the English Catholic bishops who never referred to themselves by the titles but allowed everyone else in the Catholic community to do so. In Ireland it was flouted but no prosecution was ever brought. It was repealed in 1871 the same year the Church of Ireland was disestablished.

The campaign to disestablish the Church of Ireland had been led by Archbishop (from 1866 Cardinal) Paul Cullen. It is almost impossible to overstate his influence on Ireland and Irish Catholicism worldwide. He held strong ultramontanist views and sought to bring the Catholic Church in Ireland into line in every way possible with the practice in Rome.

In Italy bishops and archbishops alike were referred to by the superlative form of reverend. So Cardinal Cullen introduced the same practice in Ireland, calling bishops and archbishops alike Most Reverend. A more cynical explanation is that he was quite happy with the distinction between bishop and archbishop when he himself, as archbishop, was a Most Reverend, abolishing it only when he became, as Ireland's first Cardinal, an Eminence.

Since the late 1860s, the practice has differed between Great Britain and Ireland. In most other English-speaking countries, including the United States, the distinction between Most and Right was maintained at least until the early nineteen-thirties.

As described in Andrew Leach's answer, and translated by Matt Gutling, in December 1930 the Vatican decreed that all bishops and archbishops receive the title Excellentiae Reverendissimae meaning Most Reverend Excellency. Bishops and Archbishops were already, in Latin, the superlative form of Reverend and while Reverendissimae is best translated Most Reverend, it could also be translated by other intensifiers such as Too Reverend, Frightfully Reverend, Enormously Reverend etc. The purpose of the decree was primarily about giving all bishops and archbishops the title Excellency, the Most Reverend bit was merely what had long been the case in Latin and many continental languages.

It was adopted in the United States fairly quickly and gradually in some other countries. The Excellency style, the main point of the decree, could not legally be adopted in the UK as only certain categories of persons were entitled to it, as officially determined, ultimately by the King, and not by the Pope.

Since the "Papal Aggression" of 1850 the Catholic hierarchy in England had been anxious to avoid any unnecessary provocation. It is possible they could have called themselves Most Reverend Excellency but there was little point. Even if the Protestant reaction of 1850-51 was unlikely to be repeated on the same scale, still there were multiple undercurrents in the early thirties suggesting caution.

The regaining of the Papal temporalities, as the Vatican State, in 1929 by the Lateran Agreement between the Pope and Mussolini made the Papacy, once again, a foreign power; making it even less desirable that it confer titles on Englishmen. Then there was the situation in Ireland with preparations in hand for the Dublin Eucharistic Congress. The Virgin Mary was being described as Queen of Ireland; although King George V's wife, also called Mary, was Queen of Great Britain and Ireland. The Eucharistic Congress was itself a great demonstration of Catholicism triumphant. Meanwhile the Church of England bishops were themselves distrusted and seen as arrogant and presumptuous, following the Prayer Book Controversy of 1928. (The Bishops had proposed amendments to the Prayer Book, Parliament had rejected them, and some bishops had threatened to turn a blind eye if vicars used them anyway.) There had also been sectarian riots in Liverpool in 1930. Any attempt by Catholic bishops to claim grander titles would certainly be controversial, and might have had unpredictable consequences.

Apart from that, many non-Catholics were coming to feel, and increasingly have come to feel, that Catholic bishops deserve, as a matter of courtesy, to be given parity of esteem with the official Church of England ones. If a Protestant bishop was Right Reverend, why not a Catholic? Any idea that Catholic bishops might be addressed with a higher respect than that given to Protestant bishops could hardly be expected to catch on outside the Catholic community.

In these days of bishops often being called by their Christian names it seems unlikely there will be any change in the near future.

Inspired by a link in Ken Graham's answer I read the Wikipedia article on Archbishops. That contains a paragraph germane to the question but which Ken doesn't quote:

Roman Catholic bishops and archbishops are styled "The Most Reverend" and addressed as "Your Excellency." In English-speaking countries, a Catholic archbishop is addressed as "Your Grace", while a Catholic bishop is addressed as "Your Lordship". Before December 12, 1930, the title "Most Reverend" was only for archbishops, while bishops were styled as "Right Reverend." ^[18]

18. Canon Law Digest, Bouscaren, Vol. 1, Page 20. Rt. Rev. Dominic Laurence Graessel. Roman Catholic Archdiocese of Baltimore. Retrieved on 2016-11-19.

The article on Graessel says

Before December 31, 1930, the title "Most Reverend" was reserved for archbishops; the other bishops were given the title of "Right Reverend." After that date, "Most Reverend" became general for all archbishops and bishops. (Canon Law Digest. Bouscaren, Vol. 1, P. 20).

Thus there are two potential dates for the introduction of "Most Reverend" for bishops.

I then searched for "31 December 1930" decree "Most Reverend" and found the Wikipedia article on the honorific Excellency which gives further details:

By a decree of the Sacred Congregation of Ceremonial of 31 December 1930^[5] the Holy See granted bishops of the Roman Catholic Church the title of Most Reverend Excellency (Latin, Excellentia Reverendissima). In the years following the First World War, the ambassadorial title of Excellency, previously given to nuncios, had already begun to be used by other Catholic bishops. The adjective Most Reverend was intended to distinguish the religious title from that of Excellency given to civil officials. ...

In some English-speaking countries, the honorific of Excellency does not apply to bishops other than the nuncio. In English law, Anglican archbishops are granted the title of Grace (Your Grace, His Grace, as for a duke), and bishops are granted the title of Lordship. The same titles are extended by courtesy to their Catholic counterparts, and continue in use in most countries that are or have been members of the Commonwealth. An exception is former British East Africa (Kenya, Uganda, Tanzania).

5. Acta Apostolicae Sedis 1931, p. 22; L'Osservatore Romano 24 January 1931.

The Acta are available online, although only in OCR form and thus do contain reading errors. The relevant decree is from what is usually called the Sacred Congregation of Rites and was indeed published on 31 December 1930:

SACRA CONGREGATIO CAEREMONIALIS
DECRETUM
DE TITULO « EXCELLENTIAE REVERENDISSIMAE »

Ssmus D. N. Pius Papa XI , eo consilio ut dignitas eorum, qui cum in Ecclesiae gubernatione, tum in ipsa Pontificis Maximi Domo principes habent partes, maiore cotidie in honore sit, Purpuratorum Patrum percontatus sententiam, qui sacris caerimoniis regundis praepositi sunt, die 11 mensis Decembris huius anni, arcessito viro hac in pagina subsignato, qui Sacrae Congregationi Caerimoniarum est a secretis, decrevit: Excellentiae Reverendissimae titulum, praeter quam Patriarchis et Latinae et Orientalis Ecclesiae, praeter quam Praelatis qui a flocculis vulgo appellantur, praeter quam Nuntiis et Internuntiis Apostolicis, tribuendum quoque esse Archiepiscopis atque Episcopis sive residentialibus sive titularibus tantum, itemque Magistro Pontificii cubiculi, Praelatis qui assident vel sunt a secretis in Sacris Romanis Congregationibus, Secretario Supremi Tribunalis Signaturae Apostolicae, Praelato Decano Sacrae Romanae Rotae ac denique Substituto Secretariae Status. Contrariis quibuslibet non obstantibus.

Datum Romae, ex aedibus Sacrae Congregationis Caerimonialis, die 31 Decembris 1930.
gg-I. Card. GRANITO PIGNATELLI D I BELMONTE,
Ep. Ostiensis et Albanensis, Praefectus
B. Nardone, Secretarius.

That is:

THE SACRED CONGREGATION FOR CEREMONIES
DECREE ON THE TITLE "MOST REVEREND EXCELLENCY"

So that the dignity of those who have the primary part of the governance of the Church, and especially of those in the house of the Pope itself, Our Most Holy Lord Pope Pius XI, after inquiring the opinion of the Purple Fathers who have been placed in charge of the rules for sacred ceremonies [i.e. the members of the Sacred Congregation for Ceremonies], has decreed by this advice, given on the 11th of December of this year, and undersigned on this page by the representative called for from those set apart for the Sacred Congregation of Ceremonies:

The title of "Most Reverend Excellency" (except for Patriarchs of the Latin and Oriental Churches, and for Prelates who are given that name by courtesy, and except for Apostolic Nuntios and Messengers), is to be given to Archbishops and Bishops, both [bishops] by residence and [bishops] by title, as well as to the Master of the Papal Household, and to Prelates who assist at or are members of the Sacred Roman Congregations, the Secretariat of the Supreme Tribunal of the Apostolic Signatura, the Prelate Dean of the Roman Roat, and finally the Substitute Secretary of State. Anything at all to the contrary notwithstanding.

Given at Rome, in the offices of the Sacred Congregation of Ceremonies, on the 31 December 1930.

gg-I [sic] Cardinal GRANITO PIGNATELLI DI BELMONTE, Bishop of Ostia and Albano, Prefect
B. Nardone, Secretary

(translation Matt Gutting)

This says that the title "Most Reverend" tribuendum quoque esse Archiepiscopis atque Episcopis sive residentialibus sive titularibus tantum, "shall be given also to archbishops and bishops who are residential and also titular."

Thus my first hypothesis is correct and prior to this decree bishops were Right Reverend, as they still are in the British Isles and most Commonwealth countries.

The question still remains as to why the decree was not taken up within the Catholic hierarchy in Britain and the Commonwealth, although the cryptic reference to "English law" in the Excellency article is probably the reason. If I find that before someone else does, I'll update this answer.