Objection 1. It would seem that there is not contracted through adoption a tie that is an impediment to marriage. For spiritual care is more excellent than corporeal care. But no tie of relationship is contracted through one's being subjected to another's spiritual care: else all those who dwell in the parish would be related to the parish priest and would be unable to marry his son. Neither therefore can this result from adoption which places the adopted under the care of the adopter.
Objection 2. Further, no tie of relationship results from persons conferring a benefit on another. But adoption is nothing but the conferring of a benefit. Therefore no tie of relationship results from adoption.
Objection 3. Further, a natural father provides for his child chiefly in three things, as the Philosopher states (Ethic. viii, 11,12), namely by giving him being, nourishment and education; and hereditary succession is subsequent to these. Now no tie of relationship is contracted by one's providing for a person's nourishment and education, else a person would be related to his nourishers, tutors and masters, which is false. Therefore neither is any relationship contracted through adoption by which one inherits another's estate.
Objection 4. Further, the sacraments of the Church are not subject to human laws. Now marriage is a sacrament of the Church. Since then adoption was introduced by human law, it would seem that a tie contracted from adoption cannot be an impediment to marriage.
On the contrary, Relationship is an impediment to marriage. Now a kind of relationship results from adoption, namely legal relationship, as evidenced by its definition, for "legal relationship is a connection arising out of adoption." Therefore adoption results in a tie which is an impediment to marriage.
Further, the same is proved by the authorities quoted in the text (Sent. iv, D, 42).
I answer that, The Divine law especially forbids marriage between those persons who have to live together lest, as Rabbi Moses observes (Doc. Perp. iii, 49), if it were lawful for them to have carnal intercourse, there should be more room for concupiscence to the repression of which marriage is directed. And since the adopted child dwells in the house of his adopted father like one that is begotten naturally human laws forbid the contracting of marriage between the like, and this prohibition is approved by the Church. Hence it is that legal adoption is an impediment to marriage.
This suffices for the Replies to the first three Objections, because none of those things entails such a cohabitation as might be an incentive to concupiscence. Therefore they do not cause a relationship that is an impediment to marriage.
Reply to Objection 4. The prohibition of a human law would not suffice to make an impediment to marriage, unless the authority of the Church intervenes by issuing the same prohibition.
Source: Summa Theologica (New Advent)