Some quick tips on naming, any zoology or taxonomy class should cover this, too. In binomial nomenclature the first name is the genus name, the second is the specific or specific epithat. Together both make up the species name. Typed, they should always be italicized like this
Avicularia avicularia. More to this is that often there will be a name and date following a species name. The name and date tells you who described and named the species, and when. If the name is not in brackets then the species has not been moved from another genus. If the name of the person who described it is in brackets, then it was moved.
So looking this up we see its
Avicularia avicularia (Linnaeus, 1758). This means that Carl Linnaeus described the species. My guess is that as one of the first of the genus described, when the taxonomy was updated the person working on it kept Avicularia as the genus name in honor of Linnaeus and/or because it was an early discription (looks to be the first) of the genus.
I'm not certain on the part of retaining the first description as a new genus name as I haven't seen that directly stated. If someone else has time to look around on iczn.org or knows for certain, feel free to share.
Update: I asked my advisor about it. It seems that this is not commonly done simply due a scientific name needing to be a noun and a adverb. So that likely accounts for not bumping into it too much.