As it currently stands, the only way for a project to be labelled "Abandoned" is for a site admin to mark it as such. Not only is this unreliable - there is a large margin of error - but it also means an author has no easy way to mark it themselves.
By letting authors mark their own projects as Abandoned, it would be quick and easy way to tell users that the project is no longer actively maintained. Say an author made a project that was a bit of a joke, but then some time later, they do not feel like maintaining it anymore because it served no purpose. Rather than let it sit there while people keep nagging the author to update to X version, the author can mark it as Abandoned, thus letting their users know what the status of the project is.
On a similar note, authors could also be able to remove the Abandoned label in the event that they may have found a new maintainer for a project after it was marked as such.