Why don't Catholics believe that Christ's atonement removed Original Sin? Original Sin is the Catholic doctrine that all human are born sinners due to the inheritance of the sin of Adam. However, Jesus Christ atoned for the sin of mankind. 

Therefore, one would assume the sin of Adam which Man inherited would be included, and thus children would not need to be baptised in order to be saved as they would be innocent.

Why do Catholics believe original sin was not washed away along with other sins?
Original Sin is washed away through Baptism

The Church believes that Christ's atonement removes original sin precisely through baptism.  More generally, in baptism the power of Christ's paschal mystery comes to bear in the recipient, who also becomes a partaker in that paschal mystery and the life of God. For example, we are told that infants are baptized not because they have committed personal sins, but because their nature is tainted by original sin:


  Born with a fallen human nature and tainted by original sin, children also have need of the new birth in Baptism to be freed from the power of darkness and brought into the realm of the freedom of the children of God, to which all men are called. (Catechism of the Catholic Church, 1250)


The Catechism of the Council of Trent tells us that "Baptism is made obligatory after Christ's resurrection."  It goes on:


  This is inferred from the authority of the Prince of the Apostles when
  he says: Who hath regenerated us into a lively hope, by the
  resurrection of Jesus Christ from the dead; and also from what Paul
  says of the Church: He delivered himself up for it: that he might
  sanctify it, cleansing it by the laver of water in the word of life.
  (Catechism of the Council of Trent, Part II on baptism)


Catholic Encyclopedia also implies that the atonement is applied through baptism in a paragraph where it argues that baptism, like original sin and the atonement, ought to be applied to all people, even infants:


  Theologians also call attention to the fact that as God sincerely wishes all men to be saved, He does not exclude infants, for whom baptism of either water or blood is the only means possible. The doctrines also of the universality of original sin and of the all-comprehending atonement of Christ are stated so plainly and absolutely in Scripture as to leave no solid reason for denying that infants are included as well as adults. (Catholic Encyclopedia, Baptism)