Whether hatred arises from envy?

Gregory says (Moral. xxxi, 88) that “out of envy cometh hatred.”

As stated above (Article 5), hatred of his neighbor is a man's last step in the path of sin, because it is opposed to the love which he naturally has for his neighbor. Now if a man declines from that which is natural, it is because he intends to avoid that which is naturally an object to be shunned. Now every animal naturally avoids sorrow, just as it desires pleasure, as the Philosopher states (Ethic. vii, x). Accordingly just as love arises from pleasure, so does hatred arise from sorrow. For just as we are moved to love whatever gives us pleasure, in as much as for that very reason it assumes the aspect of good; so we are moved to hate whatever displeases us, in so far as for this very reason it assumes the aspect of evil. Wherefore, since envy is sorrow for our neighbor's good, it follows that our neighbor's good becomes hateful to us, so that “out of envy cometh hatred” . . .

Nothing prevents a thing arising from various causes in various respects, and accordingly hatred may arise both from anger and from envy. However it arises more directly from envy, which looks upon the very good of our neighbor as displeasing and therefore hateful, whereas hatred arises from anger by way of increase. For at first, through anger, we desire our neighbor's evil according to a certain measure, that is in so far as that evil has the aspect of vengeance: but afterwards, through the continuance of anger, man goes so far as absolutely to desire his neighbor's evil, which desire is part of hatred. Wherefore it is evident that hatred is caused by envy formally as regards the aspect of the object, but dispositively by anger.

Thomas Aquinas, Summa Theologica (II-II Question 34, Article 6)