You probably have heard it said, or read, that hate is not really the opposite of love in reality because they are both founded on very strong emotions. In this way, they are related because they are both passionate. The true opposite of love or hate would be indifference, because in this case, there is no strong emotion. So hate is negative and love is positive, but they both have strong emotion at the core. Indifference does not have strong emotion at its core.
In this novel, Hawthorne explores this concept. By the end of the novel, Hester's scarlet letter "A" has taken on an entirely new significance. Whereas it was a symbol of sin and shame, it almost becomes a "red badge of courage" at the end of the novel. In the two characters affected by the scarlet letter besides Hester, Dimmesdale and Chillingworth, one represents love (Dimmesdale) and the other hate (Chillingworth) - both strong emotions. Dimmesdale is a coward, so he cannot express his love, and Chillingworth is also a coward because he hides who he is and his plan of vengeance. In the end, however, they meet the same fate, because neither of them has any balance. When Dimmesdale dies, Chillingworth cannot live because his hate is feeding off of Dimmesdale's existence and when he ceases to exist, there is no more negative emotion to nourish Chillingworth. Hawthorne seems to be implying that it is not always so easy to draw distinct lines between love and hate.