Determining xprv from xpub and child private key
This recommendation comes directly from one of security considerations from the same document:


  Note however that the following properties does not exist:
  (...) Given a parent extended public key (Kpar,cpar) and a non-hardened child private key (ki), it is hard to find kpar.


The reason for this recommendation is the fact all the non-hardened key derivation bases on some of the elliptic curve properties. One of them is that you can add some number to private key (which itself is ordinary number). When you convert the same number to the point on elliptic curve you can add it to public key (which itself is the point on elliptic curve). This new private key is exactly the private key for the new public key.

The problem is that this number we add  (parse256(IL)) can be calculated from parent public key and parent private key.

So, if we know the child private key kchild and before mentioned number parse256(IL) (which we know, because we know parent public key), then we can rearrange the equation from which this key was derived:

kchild = parse256(IL) + kpar (mod n)

and find kpar which is the parent private key.