Taking it as a general comment, I think this quote means that our deepest desires sometimes do a 360 - from being positive desires to becoming destructive emotions and actions. When we have strong desires that permeate our being, we tend to value them highly and we work to satisfy those deepest desires. The problem comes when the desire is not fulfilled completely or at all. 

We, with our human emotions and reasoning, may react badly to this. We may seek to fulfill our desire in another way - either in a socially acceptable, dignified way, or in a way that is not socially acceptable and proper. This second way can lead to behavior that borders on, or immerses itself totally in hate or some other strong emotion, because we believe we've been wronged . Consequently, we can become irrational in our thinking because of our overpowering emotions. This can lead to hateful thoughts, vengeful thoughts, violent thoughts, and if left unchecked these thoughts can turn into destructive actions.

Desire

Emotion - eNotes

I think readerofbooks has shed important light on the quote. We tend too much toward explaining texts from our contemporary perspectives while forgetting that the authors had a different milieu and construct in mind and would probably rail at the idea that something could be construed as something other than what they meant it to mean within their world view and experience.

I think further enlightenment can be gained if we think of this quotation in terms of Shakespeare's Othello. Othello's deepest desire was for Desdemona. Iago flamed that desire into a blazing inferno through falsehoods and slander. As a result, Iago caused a hate to burn in Othello that was directed--falsely--at the object of his greatest desire. To put it another way, if Othello cared (desired) less, he would have responded less to Iago's maliciousness and his hatred would have flamed less.

I wish you gave the reference in Socrates. However, it seems to me that we need to know something about Socrates tripartite understanding of people. In the Timeaus, Socrates states that people are made of three parts - mind, heart, and the apetitive parts of the body. The apetitive parts need to be ruled by the mind, because the apetitive parts desire base things. The heart is neutral, but when it is controlled by the apetitive parts, there is disaster. In light of this, the quote probably means the heart controlled by the apetitive parts of the body can produce great hate. 

I liken it to the saying, "Familiarity breeds contempt."  When we skim the surface of some emotions, never digging deep or delving into their depths, we maintain a certain aloofness that allows us to be more objective and less involved.  We seem to think clearer and our judgment is less impaired.

But, when we totally immerse ourselves in our passions, our deep desires, our longings . . . that's when we find contempt for ourselves, for others.  To become familiar with someone or something is to lose compassion and charity.  Our vision and judgment become clouded; we see "red." 

I was taught while growing up that whatever passion we don't overcome will overcome us.  It holds true for our deepest desires, some of which aren't noble.  If something ignoble overcomes us and we give in to it, we end up hating ourselves or hating others.

In this quote, desire has a really negative connotation, almost like envy, perhaps suggesting that the deepest desires of humanity would also be the most primal.

I agree with Post #4. Certainly wanting something so badly and not being able to attain it could drive a person to an equally strong emotion of hate. 

The critical word in the quote is "often." It is not a foregone conclusion that deep desire always results in deep hatred, but the possibility is there.

The potential cause and effect has been well stated by previous posts. However, the deep desire may also lead to concentrated effort and ultimate fulfillment in the realization of the desire.

We may read this as a quote relating to the dangers of an unexamined life. This is a stretch, but I'll make the argument anyway. 

Perhaps we can see this quote as warning against a course of behavior that would allow us to ignore our desires and so breed a contempt in us born of envy toward those who achieve what we secretly desire. If our deepest desire is to marry Person A, but we don't propose to Person A because we suppress our desire then someone else comes along and marries Person A. We hate this new suitor deeply as a representative both of our own weakness (not admitting to our desires) and because of a natural envy.  

I admit, however, that the most compelling interpretation of the quote is the simplest one, articulated by the post above. Our deepest desires are connected to our deepest emotions. 

The things that we desire most deeply are, almost by definition, the things we care about the most.  If I do not care about something, there is no way that I am going to be inspired to hate someone because of that thing.  Therefore, it is only the deepest desires that can lead to hate because they are connected to the things we care most about.

For me this quote refers to a desire so great that it changes within us. For example, we may want something very badly (desire it). If this desire go unfulfilled, we may become jealous of those who have it. This jealousy can turn to the hate of those who are able to possess the things which we cannot (greatest hate). Through our inability to possess the things, our desires for it change to the hate of it and those who are able to possess it.