A fellow Catholic maintains that at some time in the past the Catholic Church believed in reincarnation. Is this true?

As regards the matter of so‐called reincarnation (the belief that we have had previous lives in other bodies, or will come back in other bodies or forms), the view is clearly excluded in Scripture and by Christian Anthropology. 
 
Scripture says, It is appointed unto men once to die, but after this the judgment (Heb 9:27). “Once” is pretty clear, there are no previous deaths or lives, nor shall we face death again. “Once” cannot mean many. 
 
Further, Christian anthropology, rooted in the Scriptures, excludes the notion of reincarnation. This is not the place to set forth a full anthropology, but it is here sufficient to state that the soul is the form of the body and it does not pertain to the same soul to “form” different bodies. I am my body; it is not a mere appendage or container that can be shed or exchanged. 
 
Finally, whenever some claim the Catholic Church once taught something, a good follow‐up request is “Show it to me in writing.” For, many make unsubstantiated claims and the pressure should not be on to defend against something that never happened, but for them to demonstrate clearly the truth of their charge.