Last year during one of our RCIA sessions on the Liturgy the question was asked, “if this is the Latin rite, why is the ‘Kyrie’ still in Greek?” Stumped, we all were. Some fidgeting about how “Amen” is Hebrew and thus even the Latin Rite was never entirely in Latin ensued. But why, when the Church transitioned from Greek to Latin this part remained, well, who knows? The Catholic Encyclopedia from New Advent gives some help:
Its introduction into the Roman Mass has been much discussed. It is certain that the liturgy at the Rome was at one time said in Greek (to the end of the second century apparently). It is tempting to look upon our Kyrie Eleison as a surviving fragment from that time. Such, however, does not seem to be the case. Rather the form was borrowed from the East and introduced into the Latin Mass later. […] The first evidence of its use in the West is in the third canon of the Second Council of Vaison (Vasio in the province of Arles), in 529. From this canon it appears that the form was recently introduced at Rome and in Italy (Milan?): “Since both in the Apostolic See as also in all the provinces of the East and in Italy a sweet and most pious custom has been introduced that Kyrie Eleison be said with great insistence and compunction, it seems good to us too that this holy custom be introduced at Matins and Mass and Vespers” (cf. Hefele-Leclercq, “Histoires des Conciles”, Paris, 1908, pp. 1113-1114; Duchesne, “Origines”, p. 183). The council says nothing of Africa or Spain, though it mentions Africa in other canons about liturgical practices (Can. v). It appears to mean that Kyrie Eleison should be sung by the people cum grandi affectu.
We may suppose, then, that at one time the Roman Mass began (after the Introit) with a litany of general petitions very much of the nature of the third part of our Litany of the Saints. This would correspond exactly to our great Synapte in the Syrian Rite. Only, from what has been said, we conclude that the answer of the people was in Latin — the “Miserere Domine” of Etheria, or “te rogamus, audi nos”, or some such form. About the fifth century the Greek Kyrie Eleison was adopted by the West, and at Rome with the alternative form Christe Eleison. This was then sung, not as in the East only by the people, but alternately by cantors and people. It displaced the older Latin exclamations at this place and eventually remained alone as the only remnant of the old litany.
So … we don’t have exactly a specific answer, but at the end it looks to say that at one point it was said in Latin in the Western Church, but by the fifth century was nearly universally in Greek. That’s the history. The why, well, I’m still working on that. I’m going to drop the folks at NLM a line and see if they have any ideas.