Symmetric encryption does not have the concept of a "private key".
In the early days of public key cryptography, the NSA referred to it as "non-private key cryptography".
Even today, people often refer to symmetric vs asymmetric and private vs public interchangeably. (Yes, it can cause confusion and you will probably never see professional cryptographers like Bernstein, Green, Lange, Schwabe, Schneier, or Wilcox-O'hearn refer to it that way.)
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In the early days of public key cryptography, the NSA referred to it as "non-private key cryptography".
Even today, people often refer to symmetric vs asymmetric and private vs public interchangeably. (Yes, it can cause confusion and you will probably never see professional cryptographers like Bernstein, Green, Lange, Schwabe, Schneier, or Wilcox-O'hearn refer to it that way.)
https://en.wikipedia.org/wiki/Symmetric-key_algorithm#cite_n...
The author had multiple errors; it isn't beyond the limits of intellectual generosity to assume they meant symmetric key instead of private key.
128 bit EdDSA would have about the same security as a 64 bit block cipher, which we would consider broken. So I'm in full agreement there.
128 bit RSA? Totally useless.
128 bit AES? Not a concern. Usually you look at the padding, block mode, and authentication instead.