I repeat: there is a qualitative difference between "lonliness" and "needing help". Well, maybe not so much in "authoritative teaching" when you read the balance of the contextual paragraph, which seems to answer your "figure out". Card. Ratzinger writes: 
"He needs a helpmate who will be his partner. The term here does not refer to an inferior, but to a vital helper. This is so Adam's life does not sink into a sterile and, in the end baneful encounter with himself".
You figure out what it means for you. To me, it means that women were and are created so that man avoids bestiality ("a loneliness which the presence of the animals is not able to overcome"), acheive reproduction ("so that Adam's life does not sink into a sterile...) and avoid solipsistic, self pleasuring (...and, in the end, baneful encounter with himself").
This is the "helpmating" (or help-in-mating) authority you and R&R hold as authoritative (By the way, that was even before Eve "seduced" Adam.  It gets worse).