Hi Medicine Woman! I've missed you!
Your analysis of the word virgin, while generally true, isn't precisely accurate. Virginity does refer to youth, and being unmarried, but it does also refer to not having had sexual intercourse.
Mary wasn't merely said to have given a virgin birth, but was also said to have been a perpetual virgin. If you were right regarding how we should read "virgin," then this would mean either that she was perpetually young, or perpetually unmarried. We know both of these to be untrue. Mary grew old, and she also marriged Joseph.
The perpetual virginity of Mary has been held by the Catholic Church since its early days, and was held by
•St. Irenaeus (III, 21; see Eusebius, Church History V.8),
•Origen (Adv. Cels., I, 35),
•Tertullian (Adv. Marcion., III, 13; Adv. Judæos, IX),
•St. Justin (Dialogue with Trypho 84),
•St. John Chrysostom (Hom. v in Matth., n. 3; in Isa., VII, n. 5);
•St. Epiphanius (Hær., xxviii, n. 7),
•Eusebius (Demonstrat. ev., VIII, i),
•Rufinus (Lib. fid., 43),
•St. Basil (in Isa., vii, 14; Hom. in S. Generat. Christi, n. 4, if St. Basil be the author of these two passages),
•St. Jerome and Theodoretus (in Isa., vii, 14),
•St. Isidore (Adv. Judæos, I, x, n. 3),
•St. Ildefonsus (De perpetua virginit. s. Mariæ, iii).
Mary's virginity was defined in the third canon of the Lateran Council in 649AD.
Moreover, the Gospel accounts themselves indicate that indicate that Mary's virginity referred to her not having had sexual intercourse. Luke 1:34-35 says "Mary said to the angel: How shall this be done, because I know not man? And the angel answering, said to her: The Holy Ghost shall come upon thee, and the power of the most High shall overshadow thee. And therefore also the Holy which shall be born of thee shall be called the Son of God." The phrase "I know not man" was a euphamism that meant she hadn't had intercourse.
What you have said is true, "virgin" did refer to young women, and unwed women, but it did so because such women would have been understood to have not yet engaged in sexual intercourse.