This article about a caterpillar specialist claims:
There are roughly sixty-five hundred species of mammals, nine thousand species of amphibians, and eleven thousand species of birds. These are what people tend to think of when they picture the world’s biodiversity. But the planet’s real diversity lies mostly beneath our regard. The largest family of beetles, the Curculionidae, commonly known as weevils, contains some sixty thousand described species; another beetle family, the Tenebrionidae, comprises twenty thousand species. It is estimated that in one family of parasitic wasps, the Ichneumonidae, there are nearly a hundred thousand species, which is more than there are of vertebrates of all kinds.
I am suspicious of this claim for two reasons:
First, there is no established single definition of what constitutes a "species." So maybe they are applying one definition to vertebrates that is not reasonably comparable to the definition being used here for insects?
The article seems to say that, at least when it comes to lepidoptera, entomologists have decided that every polymorphism of a single gene (CO1) constitutes a different species, which to me sounds like a fast-and-loose definition.
Whatever the definition, I am skeptical that entomologists can keep track of tens of thousands of samples of "unique species" of a single family of insects in such a way as to ensure there are no duplicates. E.g., 60,000 "descriptions" of beetles they are confident are unique? (Much less so "unique" as to constitute different species?)