According to this system, love is nothing but the desire of happiness to another person, and hatred that of misery.

The desire and aversion constitute the very nature of love and hatred.

They are not only inseparable but the same.
But this is evidently contrary to experience.

For though it is certain we never love any person without desiring his happiness, nor hate any without wishing his misery, yet these desires arise only upon the ideas of the happiness or misery of our friend or enemy being presented by the imagination, and are not absolutely essential to love and hatred.

They are the most obvious and natural sentiments of these affections, but not the only ones.