Yes, I understand what you were saying, and sorry if the quote I pulled removed some of the context of your point.
That being said, I still don’t fully agree with this statement. This is just as much true for the species level as it is for any other level, or rather, no other level is any more or less arbitrary than the species level. Taxonomic levels are often ill defined, inconsistent, and, to an extent, arbitrary, but that doesn’t mean there isn’t a method to the madness for why things are placed at one rank instead of the other.
If I’m understanding you correctly, I think what you mean is as follows (correct me if I am wrong): The species level is the the taxonomic group that lay people have the firmest concept of. And so, if that level is subject to constant revision, people may get confused or discouraged by the constant change.
In part, I’m confused by your use of the term “biological meaning”. If anything, I think relying on outdated taxonomy can result in the biological significance of species being obscured, something I think @elsemikkelsen was alluding to: