But it doesn’t. At least not sin, “in the proper sense.”
The Catechism affirms that (CCC 404), “By yielding to the tempter, Adam and Eve committed a personal sin, but this sin affected the human nature that they would then transmit in a fallen state.”
What is being transmitted is a fallen humanity.
It is a sin which will be transmitted by propagation to all mankind, that is, by the transmission of a human nature deprived of original holiness and justice. And that is why original sin is called “sin” only in an analogicnal sense: it is a sin “contracted” and not “committed” - a state and not an act.
Note that sin in any positive sense is not being transmitted, nor is guilt. Original sin is sin, “in an analogical sense.”
Even after baptism we remain members of fallen humanity, and it is this fallen humanity which is passed on.
Original sin is rnot just covered up.
405 Although it is proper to each individual,295 original sin does not have the character of a personal fault in any of Adam’s descendants. It is a deprivation of original holiness and justice, but human nature has not been totally corrupted: it is wounded in the natural powers proper to it, subject to ignorance, suffering and the dominion of death, and inclined to sin - an inclination to evil that is called concupiscence". Baptism, by imparting the life of Christ’s grace, erases original sin and turns a man back towards God, but the consequences for nature, weakened and inclined to evil, persist in man and summon him to spiritual battle.