Asnehana is one of the names of God Śiva (Siva). He is the creator of the universe, the Supreme entity, who showers his fatherly affections and blessings over all gods, demons, human beings, animals –all living creatures. So he is conceptualised as an affectionate, universal, divine father-figure. Hence he comes to be known as Snehana (one who is affectionate).
Asnehana (one who is not affectionate, that is, ruthless) is just the opposite of Snehana. Śiva can be benevolent and fatherly towards all the world of creation, but at the same time, he can also assume a rudrarupa (a terrible, wrathful form) to punish the evil-doers and the prodigal children. It is for the greater benefit of the world, he assumes his destructive self, in order to bring retribution to evil. This terrible form of Śiva is referred to as ‘Asnehana’.