Now one who is unable to beget, through being a eunuch or impotent, suffers especially from the absence of children of his own begetting. Therefore he is especially competent to adopt someone as his child. But he is not competent to adopt. Therefore adoption is not the taking of someone as one's child.

???  This makes no sense to me.  It seems in one sentence he is saying that someone who is unable to beget is competent to adopt, and then he says the complete opposite in the next sentence?

First, I must point out that you're quoting the objection rather than the reply to said objection.
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However, that doesn't really clear much up. It seems to me, from a quick reading of this entry, that adoption at that time was not for the sake of the child, but for the sake of a grieving adult (due to loss of a biological child). So, you'd only be eligible to adopt if you've lost a biological child or grandchild.
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Seems very odd to me as it's quite different now, but that's what it seems to be saying. If I'm not reading it correctly, feel free to explain it to me. : )

It doesn't matter what St Thomas said 600-700 years ago, adoption today is supported by the Church both philosophically and through Her many Catholic charities.  St Thomas lived in the middle ages, the most Catholic time in all of history.  Probably weren't too many orphan children or unwanted pregancies in his day.  Any children who were born out of wedlock were taken care of by the extended family, who normally lived close together and operated as a team. 

Now one who is unable to beget, through being a eunuch or impotent, suffers especially from the absence of children of his own begetting. Therefore he is especially competent to adopt someone as his child. But he is not competent to adopt. Therefore adoption is not the taking of someone as one's child.

???  This makes no sense to me.  It seems in one sentence he is saying that someone who is unable to beget is competent to adopt, and then he says the complete opposite in the next sentence?

That translation uses the same word to translate two distinct words of the Latin:
Super Sent., lib. 4 d. 42 q. 2 a. 1 arg. 4:

ille qui non potest generare, ut spado vel frigidus, maxime patitur defectum in filiis naturalibus. Ergo ei maxime competit assumere in filium aliquem. Sed non competit adoptare ei.

The sense is that the impotent (note: he doesn't say sterilis, but spado vel frigidus or "eunuch or frigid (person)", which is impotency) should be entitled to children (maxime competit assumere or "most entitled to assume"), but they should not be able to adopt (presumably because of their impotence).
So, St. Thomas argues that the impotent (not the infertile) should not be able to adopt. Perpetual impotency impedes marriage anyways.

St. Thomas's understanding of adoption is that it is to replace lost children (not children never had):

This is corroborated by his

Reply to Objection 4. ... greater is sorrow for children lost than for children one has never had. Wherefore those who are impeded from begetting need no solace for their lack of children as those who have had and have lost them

This is St Thomas' opinion but it's not the Church's, so his opinion doesn't matter in this case.  This isn't a moral issue but a social one, therefore his opinion is outdated.

Sterility/infertility would be an "accidental impediment".
In summary:

• Adoption is chiefly for replacing lost children.
• The impotent cannot adopt.
• St. Thomas doesn't deny the sterile/infertile can adopt.

Thank you for this.  I wish you hadn't posted anonymously.

I wonder why you ask it.

Seeking counsel as to whether it's something my wife and I are called to

With respect, do you really think it could possibly be against the faith?

The hispanic culture seems to frown upon it. In fact, in Mexico the only way to adopt is if the child is a true orphan; both parents must be deceased.

The Abelites, whom St. Augustine condemned, were a very strange sect of married, perpetually continent couples who each adopted a boy and a girl:

LXXXVII. There is, or rather there was, an unsophisticated heresy in our countryside, that is, around Hippo. It gradually diminished, but continued to exist in a single small village, in which only a few people, but the whole population, were its members. Now all of these have been corrected and have become Catholics, and no one from that error survives. They were called the Abeloim in the Punic form of the name. Some say that they were named after the son of Adam who was called Abel; hence, we can also call them Abelians or Abeloites.

They did not have intercourse with their wives, and they were, nonetheless, not permitted by the teaching of this sect to live without wives. Husbands and wives, therefore, lived together under the vow of chastity and, by the agreement of their union, adopted for themselves a boy and a girl to be their successors. If any of these died, others were chosen to take their place, provided, of course, that two of the opposite sex took the place of the other two in the same household. If either of the parents died, the children served the one remaining until he or she also died. After that parent's death, they likewise adopted a boy and a girl. There was never a lack of children for them to adopt, since their neighbors on all sides bore children and gladly gave them their poor children in the hope that they would become their heirs.

Were they incestuous, or is St. Augustine condemning their practice of adoption, their vow of chastity, or both?