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. 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 [sic]. And that is why original sin is called "sin" only in an analogical sense: it is a sin "contracted" and not "committed" - a state and not an act.
Catechism of the Catholic Church ... III Original Sin ... Paragraph 404
The catechism here makes clear that sin is a matter of the transmissible human nature. Sin is a matter of humanity, of flesh and blood. And the flesh and blood, the humanity, that is inherited by natural generation, is that in which sin is transmitted.