There are two ideas that come to my mind when I read this famous quote. The first concerns what can sometimes happen in a loving relationship and the second concerns the inclination of people to condemn behavior that they themselves are drawn to.
When two people enter into a deep and passionate relationship, there can be seeds of destruction already planted. As a relationship goes on, sometimes what attracts one person to another is what causes one person to hate the other at the end of the relationship. Often this is because opposites tend to attract. In the long run, though, a person who has characteristics opposite to yours can make your love turn to hate. For example, I am a quite introverted person who might have been attracted to a very extroverted person. But had I married that extrovert, as time went on, I might have found it difficult or impossible to live with all that extroversion, with my love turning perhaps first to annoyance, and then, perhaps, gradually, to hate. My observations over the years of couples who have parted have led me to the conclusion that the more passionately they felt about one another at the beginning, the deeper their hatred at the end. In other words, our deepest feelings are a two-edged sword, the deeper they are, the more easily they can turn to the deepest of contrary emotions.
There is also a human tendency to strongly oppose behavior that we secretly long to indulge in. When a desire is frowned upon by the society in which a person lives, this tendency is particularly pronounced. This is our means of fighting an undesirable desire and of allowing others around us to believe that we oppose the behavior, too. There are countless examples of this in the present day. Some politicians, for instance, who have strongly and passionately opposed gay marriage, have turned out to be gay themselves. They are perhaps fighting their own deep desires as well as persuading others that they do not have them. Those people who fight passionately against marijuana, alcohol, or gambling might very well be people who are most tempted by these. I do not mean to suggest that every time we see someone passionately against something that this necessarily implies he or she is railing against a deep desire, but certainly, this does turn out to be the case in many instances.
What Socrates had to say was quite profound in either instance. Our deep loves can turn to hates and our deep desires can turn to a hatred of them.