Being is not a genus in the strict sense because there is no categorial nature that is common to all beings. This paper argues that Aristotle nevertheless treats being as a genus, that this treatment is what he means in Metaphysics Gamma by the science that studies being qua being, and that what is common to all beings is not some particular nature, but their each having a nature. This nature is its ousia, and in Gamma, these ousiai are the primary beings to which other beings are related, though later in the Metaphysics, in a different stage of this science, “ousia” is limited to categorial ousia. It is necessary for being to be a genus in order that metaphysics can treat the principle of non-contradiction.
Halper, Edward C., "Aristotle's Generic Being" (2009). The Society for Ancient Greek Philosophy Newsletter. 368.