I always believed it but never thought it through.
Even if Mary was conceived sinless, why is it so important that she had remained a virgin all her life? Sex within the confines of marriage is not a sin.
I'm going to accept the "even if" comment as rhetorical. The Cathecism states:
508 From among the descendants of Eve, God chose the Virgin Mary to be the mother of his Son. "Full of grace", Mary is "the most excellent fruit of redemption" (SC 103): from the first instant of her conception, she was totally preserved from the stain of original sin and she remained pure from all personal sin throughout her life.
509 Mary is truly "Mother of God" since she is the mother of the eternal Son of God made man, who is God himself.
510 Mary "remained a virgin in conceiving her Son, a virgin in giving birth to him, a virgin in carrying him, a virgin in nursing him at her breast, always a virgin" (St. Augustine, Serm. 186, 1: PL 38, 999): with her whole being she is "the handmaid of the Lord" (Lk 1:38).
511 The Virgin Mary "cooperated through free faith and obedience in human salvation" (LG 56). She uttered her yes "in the name of all human nature" (St. Thomas Aquinas, STh III, 30, 1). By her obedience she became the new Eve, mother of the living.