There is no end of people today who argue that in the text in Isaiah: “Behold, a Virgin will conceive and bear a son,” the term “Virgin” merely means a young woman. This is not a new or clever argument, but is answered in the Church’s tradition. The best analysis I have seen, however, is Cardinal Franzelin, a peritus at Vatican I, whose work I present on this subject:
De Verbo Incarnato
Thesis XV, II
1) We ask in what way is the revelation that is consigned to the Scriptures disposed in regard to this chapter of doctrine. The principle place pertaining to this is the prophecy of Isaiah (Is. VII:14): “Behold a Virgin will conceive and bear a son, and his name will be called Emmanuel … which means God is with us,” as is added in Matthew’s Gospel (I:23). In Hebrew this is literally: “Behold a Virgin, herself pregnant and giving birth to a son, and she will declare his name (matter, being) ‘God is with us.’”
a) The prophecy refers to Christ and his Virgin mother; for it is clear from the nature or rather more from the divine and human natures of the son. Emmanuel is certainly a name, which no man in the Scriptures is said to have born, it was not imposed from the will or external circumstances, but denoted by a name through the biblical use of speech and its intimate nature which is preached. (cf. Is. IX:6) Meanwhile this also was omitted, the son Emmanuel (Is. VIII:8) is hence said to be he whose land is Israel, I say the promised messiah.  For this reason, the conception and birth of this Emmanuel should be declared to be above the laws of nature, on which we will speak a little later. Therefore, St. Matthew I:22-23, that argument alone suffices which he eloquently teaches that the prophecy pertains to Christ and his miraculous conception and birth. For that reason, both the Holy Fathers and all Christian interpreters understand this prophecy.
b) The mother of the Emmanuel is certainly called a Virgin, and with an article ἡ παρθένος, to which the quality designated by this noun fits in a singular and excellent mode. For in six places, where besides this name is found, and the meaning present is no other than a Virgin: Genesis XXIV:3; Exodus II:8; Ps. LXVII (Heb. 68):26; Cant. I:3; VI:7; Prov. XXX:19. Nay more, lest a very serious matter be reduced to the trifles of grammarians, the determination of the true sense of Isaiah in no way depends from the exclusive meaning of the name considered in itself; for in this place the mode is of a solemn announcement demands a singular prodigy, so necessarily the meaning of a virgin, lest the prayer would be inept. For this reason, the Jews even to the controversies against Christians (as it is clear from the Septuagint and from the manner of citing of St. Matthew), all Christians even to the birth of rationalism, understood the prophecy to be about Christ and his supernatural, miraculous conception from a Virgin. Lastly, again the very interpretation of the Evangelist (Matth. I:22, 23) is sufficient to prove this by itself.
c) With these being fixed already, the words: “Behold, a Virgin will conceive” necessarily must be understood in the sense composed both with Isaiah and most evidently with St. Matthew, where either from the Evangelist or from the appearance of the Angel to St. Joseph the prophecy is declared. But now, if this is conceded, no also the other word “and will give birth” necessarily must be understood in the same sense. Therefore both with Isaiah and Matthew, A virgin remaining a Virgin is said not only to conceive but also to give birth. Therefore, the most holy mother was revealed just as was ἡ παρθένος. A Virgin through excellence before the conception and in the conception of the Emmanuel, so remained in the same integrity even in birth. What we say in the major and minor proposition, is clear in the first place from the words themselves, especially as and what is read in St. Matthew: “behold a Virgin herself (which the prophet looks to in the present) pregnant and giving birth.” Besides these words were advanced by Isaiah after he offered the choice to the king of a sign completed above the order of nature. When the king refused to ask for it, the prophet intended to prophecy a characteristic prodigy: “for that reason (because you refuse to ask) the Lord himself will give you a sign (worthy by his omnipotence and infinite wisdom); behold a Virgin, etc.” After dividing the sense, not only would he announce no miracle, but something common and obvious with solemnity of words, which would be unsuitable for a prudent man, much more a prophet; but in the composed sense, which words alone are advanced, he announces something contradictory according to the laws of nature, “a Virgin, pregnant and giving birth,” which, therefore, could be effected by the almighty alone, and duly is a miracle corresponding to the solemnity of the prophetic oration. Therefore, with Matthew it is thus proved that he was not only conceived, but also born virginally. The Evangelist enunciates two distinct facts, the conception without the work of man through the power of the Holy Spirit, and the birth of a son; both however are said to have come to pass, that the prophecy would be fulfilled about a Virgin pregnant and giving birth. Therefore with the witness of the Evangelist, just as the prophecy foretold a pregnant Virgin by a supernatural mode of conception without the loss of inviolate virginity, so the prophecy foretells the supernatural mode of birth in regard to the Virgin giving birth without wound to the same virginity.
It is certain, therefore, from revelation of a most intact virginity preserved even in birth is from the Scriptures themselves. That the very thing by reason could not be arranged in a dissimilar way from the narration of St. Luke; both because the words of the angel to the Virgin (Luke I:31) “Behold, you will conceive in the womb and bear a son,” are themselves an application of the prophecy of Isaiah, and therefore the name and quality of a virgin ought to be understood, and because solicitude for the blessed Virgin for preserving her virginity (v. 24: “how shall this be?”) is related to the whole thing which preceded “You will conceive and bear a son;” and also therefore, even the power of the Holy Spirit and the overshadowing of the most High (v. 35) in the response of the angel is extended to the preservation of her virginity in both, that is not only in the conception but even in birth.
 If we were to give, the son of king Achaz could absolutely be called in these very words: “thy land o Emmanuel,” certainly could not be meant of another among the sons of the king, unless he was going to succeed in rule. But this was certainly Ezechias, and he was not going to be born of time but was still a new adolescent at least in those years, as St. Jerome adverts, or duly more increased with the passing of years.
 In the last place some reckon it comes about that the name in Hebrew, in itself does not provide the meaning of virgin, but of any young girl. But even if by chance the noun there will mean abstractly a young girl for the Hebrew as well as for the Septuagint, Syriac and Latin interpreters, certainly it retains the meaning of virgin; for it means an unmarried girl, diligently guarded, to which it is clear no man has gone into her, unless someone procures for himself a very secret way by arts of deception. Thus: “There are three difficult things and the fourth I am altogether ignorant of (The Hebrew has there are three more wonderful things to take, and the fourth I know not): the way of the eagle in heaven, the way of the snake over the rock, the way of a boat in the midst of the sea, the way of a man in adolescence.” (In Hebrew the words can be read: the way of a man to a virgin.).