Liquid said it is a very soft wood, not it is a soft wood. Yes, balsa is a hardwood, but that only means that it does not keep its leaves during winter like pine and redwood. This has nothing to do with the strenght of the material as the description "hardwood" implies.
Anyway, balsa is not easy to work with, and it is not recommanded for structural woodware like chair, desk, and shelf. It is not cheap either, and if you want light weigth, you can use other materials.