Tyrannical Sky Tigers, despite not eating humans or exhibiting any type of "demonic" behavior are still considered demonic beasts. For all demonic beasts are different from regular beasts and much stronger, even more so than human cultivators. What cultivators consider "Holy Beasts", by definition, can only be summoned from the heavens. As in, they do not naturally exist in the wilds. Therefore, even vegetarians like rabbit demonic beasts or species like the Tyrannical Sky Tiger that don't bother with others unless intruded upon, are still considered as such. To say it kindly, it is because they are a potential danger to human society. To put it harshly, it is so that no one will oppose even if you kill or cage them, for they are "demonic", and "demonic" by definition is bad or evil.