That is the 'Immaculate Conception', as I understand it. I didn't know it for years, my assumption was that it was Jesus' birth. It wasn't, it was Mary's. That is this teaching - she was conceived without sin, so Jesus could be a perfect sacrifice.
Mary didn't need to be sinless. She only needed to be a virgin and that was prophesied. If she had needed to be sinless, and all that other stuff about her was necessary, then that would have been prophesied as well. God would not have neglected to include something to critical to the birth of Jesus as that, if it were the case.
Jesus shared fully in our humanity. He was tempted in every way, just as we are and yet was without sin.
Hebrews 4:14-16 14Since then we have a great high priest who has passed through the heavens, Jesus, the Son of God, let us hold fast our confession. 15For we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin. 16 Let us then with confidence draw near to the throne of grace, that we may receive mercy and find grace to help in time of need.
Based on the Catholic's assumption that this indeed happened, whatever it was that God did for Mary and her mother that Mary could be conceived without sin, God could have done for Mary and Jesus. If Jesus were limited by his mother's sinfulness and He was who He was, then how could a mere mortal born of a human mother and father not be limited by HER parents sinfulness?
If Catholics would only think this through, they might just start asking some relevant questions. As of yet, I have not received a real answer to this question.