Why is Mother Mary considered to be born without sin and we are, with sin? If Jesus died for our sins, shouldn’t we also be born without sin?

Your question mainly concerns two important theological concepts: Original Sin and the Immaculate Conception.

Original Sin refers to the sinful condition we are all born in, which is a consequence of the sin of Adam and Eve. Through them, “sin entered the world” (Romans 5:12), and we as their children have been implicated in their sin. The Catechism speaks about this in detail in sections 385-390 and 396-412.

It is true that Jesus died for our sins, but in order for us to receive this freedom from sin, we must “enter into” his death, which comes only through baptism. St. Paul explains this in his letter to the Romans:
“Are you unaware that we who were baptized into Christ Jesus were baptized into his death? We were indeed buried with him through baptism into death, so that, just as Christ was raised from the dead by the glory of the Father, we too might live in newness of life. For if we have grown into union with him through a death like his, we shall also be united with him in the resurrection. We know that our old self was crucified with him, so that our sinful body might be done away with, that we might no longer be in slavery to sin. For a dead person has been absolved from sin. If, then, we have died with Christ, we believe that we shall also live with him” (6:3-8).

Next, let’s look at your question about Mary. Because of her purpose and mission in the history of salvation, Mary was given a special and unique grace by God–we call this grace the Immaculate Conception. That means that, from the very first moment of her existence, Mary was preserved from sin and its corruption–that is, she was conceived without Original Sin. God did this by looking at the future merits of Christ on the Cross and bestowed those graces upon Mary–which is why we (following the angel Gabriel) call her “full of grace” (Luke 1:28).

Why would God do this specifically for Mary? For one, it was fitting that the Mother of God–the one who would bear God in her womb–should be preserved from all the stains and corruptions of sin. She is the living Ark of the Covenant, the God-Bearer. There’s another very important reason, though: Mary’s “yes.” “Behold, I am the handmaid of the Lord. May it be done to me according to your word” (Luke 1:38). Mary’s “yes,” her Fiat (“let it be done”) had to be a complete “yes.” It had to be a free “yes.” Sin is always a kind of bondage, a slavery. We can only say “yes” to God as much as we are free from sin. By preserving Mary completely from all sin, she had the freedom to say “yes” so completely that God himself came into the world as a child in her womb!