What is the reasoning for Latin being the official language of Catholic Mass?

The Church in the first millennium comprised five ancient Sees, of which Rome was only one. There other four were Alexandria, Constantinople, Antioch, and Jerusalem. Their jurisdictions were defined in the canons of the 1st and 2nd Ecumenical Councils.

Greek was the language of the eastern Sees, Latin the language of the Roman see. So naturally the Roman See used Latin and the rest of the Church used Greek.

Even though the eastern Patriarchates are today much diminished in size, all but Antioch still cling to Greek as their official ecclesiastical languages.

While formulating this question I found this reading that helped me answer one of my questions, why the church had retained one single language across the world for so long.

The scriptural reasoning that was used to defend keeping the Mass in one language, Latin, for so long was Genesis 11:7, The story of the Tower of Babel.

Come, let us go down and there confuse their language, so that they may not understand one another's speech.”

Since different languages was punishment because of sinning against God, the Church wanted to do away with sin and therefore different languages.

The Holy Sacrifice of the Mass: Dogmatically, Liturgically and Ascetically Explained (1902) by Fr. Nikolaus Gihr writes in the first footnote of §32, "The Language Used in the Celebration of the Holy Mass" (p. 319-328):

Whether the Apostles celebrated the Holy Sacrifice in the language of each individual nation or only in the Aramean (Syro-Chaldaic), Greek and Latin languages cannot be determined with certainty. In any case, from the first four centuries no liturgy can be shown composed in any other than the three languages of the inscription of the Cross [i.e., Hebrew, Greek, Latin]. In the West, for example, in Italy, in Germany, in Spain, in France, in England, Latin was at all times the liturgical language. Toward the end of the ninth century Pope John VIII. (872-882) permitted the Moravian Slavs, converted by Sts. Cyril and Methodius, to celebrate the liturgy in their (Slavonic or Glagolitic) native language, and that probably in order to prevent their apostasy to the Greek Schism. In the East also the Church later on permitted some schismatics and heretics, who had returned to the unity of the Church (for instance, the Copts, Armenians, Ethiopians), to retain their native language in the liturgy.

Fr. Adrian Fortescue's 1917 The Mass: A Study in the Roman Liturgy says, in §3 "Latin as a Liturgical Language" of the ch. "The Origin of the Roman Rite," that (p. 126-127):

Latin was apparently first used by Christians in Africa. Pope Victor I (190-202), who was an African, is generally quoted as the first Roman to use it.³ Novatian (c. 251) writes in Latin; since about the third century this becomes the usual and then the only language spoken by Christians at Rome. When it replaced Greek in Church is disputed. Kattenbusch dates it as the liturgical the second half of the third century,⁴ Watterich,⁵ Probst⁶ and Rietschel⁷ think that Greek was used till the end of the fourth century. In any case the process was a gradual one. Both languages must have beenused side by side during a fairly long period of transition. A certain Marius Victorinus Africanus, writin about 360 in Latin, still quotes a liturgical prayer in Greek.¹ The Bible existed only in the Greek Septuagint for some time.² The lessons were read in Greek at Rome, at any rate on some days, till the VIIIth century;³ some psalms were sung in Greek at the same time.⁴ Amalarius of Metz⁵ († c. 857) and Pseudo-Alcuin⁶ still mention Greek forms. The creed at baptism may be said in either Greek or Latin, at the convert's discretion, according to the Gelasian Sacramentary.⁷ But our present Greek fragments⁸ are later interpolations.

By at least the 12^th century, the Latin language in the Roman (i.e., Latin) Rite was most widely used, and, as Fr. Gihr writes (p. 319-320), it was attacked by heretics and schismatics:

The Mass considered in itself could assuredly be celebrated in any language, but by the Providence of God the Latin language has become, and still continues to be of all languages the most widely diffused for divine worship.² The very ancient practice of the Church of celebrating Mass in the West, not in the living language of the country, but in a dead language, that is, in Latin, for the most part a language unintelligible to the people, has since the twelfth century to the present epoch been frequently made the subject of attack.

Between the 12th century and the Council of Trent, there were some oddities or abuses like half-Latin, half-vernacular sequences (cf. Fortescue p. 275), but the Council of Trent curtailed these by saying (Session 22, can. 9):

Canon IX.—If anyone saith, … that the mass ought to be celebrated in the vulgar tongue only… let him be anathema.

Regarding homilies: These are meant for the instruction of the faithful, and thus they were in the vernacular.

For the most recent scholarship on this topic, see:

• Reid, Alcuin. The Organic Development of the Liturgy: The Principles of Liturgical Reform and Their Relation to the Twentieth Century Liturgical Movement prior to the Second Vatican Council (Farnborough, Hants.: St. Michael’s Abbey Press, 2004).

International Federation Una Voce (FIUV)'s position paper:

• PP 7: Latin as Liturgical Language (revised 10/10/12)

FIUV is an international organization promoting the pre-Vatican II Roman Rite Mass in Latin.

I don't think that there really is any scriptural reason for using Latin as the official language of the Church.

However, the Church has been located in Rome since St. Peter was crucified there in about 64 A.D. In Ancient Rome, the language that was the official language was that of Latin.

The reason Mass has been said in Latin for so long is that it is the official language of the Church, even if it is no longer the official language of Rome.