Sympathy constitutes friendship; but in love there is a sort of antipathy, or opposing passion. Each strives to be the other, and both together make up one whole.

This quote is saying that sympathy helps to create friendship by bringing people together, while love has an opposite quality which is also attractive. In love, two people get so close that they each want to become the other person. Together, though, this creates a strong connection and an inseparable, complete union of two people.