One of the texts commonly thought to disprove the doctrine of universal salvation is the following:
καὶ ἀπελεύσονται οὗτοι εἰς κόλασιν αἰώνιον, οἱ δὲ δίκαιοι εἰς ζωὴν αἰώνιον
Then they will go away to eternal punishment, but the righteous to eternal life (NIV)
Two points can be made about a universalist interpretation of this text. The first is that αἰώνιος, here translated "eternal," does not typically mean that except in reference to God; otherwise it describes the quality of belonging to the age to come (in contradistinction to this present age). Thus the idea is that Jesus is here describing the punishment/life of the age to come, and not making a quantitative statement with the adjective αἰώνιος. The second point is that κόλασις, here translated as "punishment," is not retributive in nature but rather administered for the sake of instruction. Κόλασις is aimed at the good of the person receiving it, and so in principle it could not be eternal.
In support of both points, I here cite Ilaria Ramelli's tremendous (and impressive) work, The Christian Doctrine of Apokatastasis (Brill, 2013), which covers the development of the doctrine of universal salvation from New Testament times to the early middle ages in about 900 (!) or so pages.
Ramelli notes in an extended discussion, beginning at pp. 25ff., that αἰώνιος does not mean "eternal" unless used in reference to God. Just as αἰών does not refer to eternity but to a period of time, so also αἰώνιος does not mean "eternal" but rather "pertaining to an age." For instance, Rom 16.25 affirms that a mystery was hidden "from time immemorial" (χρόνοις αἰωνίοις), not "eternal times." And 16.27 affirms that God has glory through Jesus Christ "through the ages" (εἰς τοὺς αἰῶνας), not "through the eternities." As it is being used in this discussion, there could not be multiple eternities, since an eternity is in principle supposed to be endless. A word which does mean "eternal" is ἀι΅διος, but which the NT does not use to describe the punishment.
In evidence of this point we appeal to Origen who affirms that one may pass from ζωὴ αἰώνιος, from "the life of the aeon," from "eternal life," into an existence beyond the ages. As Ramelli notes, For "αἰώνιος life" will always be the life in the next aeon, in Christ, but even that aeon will finish and therefore after "life αἰώνιος" there will come the eventual apokatastasis, in which all will be in the Father, or better in the Holy Trinity, and God will be "all and all" (Ramelli 2013, p. 160). Origen, as a native speaker of the Greek language with philosophical and literary erudition, interprets the phrase ζωὴ αἰώνιος as referring to life within an age, not endless or interminable life.
In support of the distinction of κόλασις from retributive punishment, we may here cite two sources. The first is Aristotle, who distinguishes between κόλασις and τιμωρία: the former "is inflicted in the interest of the sufferer," but the latter "in the interest of him who inflicts it, that he may obtain satisfaction" (Rhet. 1359b13, qtd. in Ramelli 2013, p. 32). The same point is likewise made by Plato in Gorg. 476A-477A, who writes that κόλασις is good for the person suffering it, since it makes him better (ibid.). Ramelli also emphasizes that the New Testament never uses τιμωρία to describe the αἰώνιος punishment.
This same distinction carried over until the time of the New Testament, for Clement of Alexandria observes the same distinction. He writes: God does not punish [τιμωρεῖται] -- since punishment is the retribution of evil with further evil [that is, suffering or loss] --, but corrects [κολάζει] for the sake of those who are corrected, both in general and singularly (Strom. 7,16,102,1-3, qtd. in Ramelli 2013, p. 127).
What we have in these cases, then, are intelligent native speakers of Greek -- which honor no contemporary scholars or translaters can claim for themselves -- who understand and elucidate the distinction between these two terms, which the New Testament uses. The wise thing to do, to my mind, is to follow after them and appreciate the point the universalist makes about κόλασις and αἰώνιος.