Why fear is the opposite of desire and not disgust? Wikipedia page on desire has the following passage:


  A 2008 study by the University of Michigan indicated that, while humans experience desire and fear as psychological opposites, they share the same brain circuit.


Personally, I feel that fear and disgust  are different. Former is what you can feel when there is something dangerous or risky. Latter is when you just perceive something like awful smell or flavor.

So, why and how fear and not disgust is the opposite of desire?
Just because two phenomena (partially!) share brain architecture does not mean they are experientially similar or opposite. There is little understanding of how neuronal activity creates conscious experiences. There is a lot of controversy in taxonomies of emotion because it is not clear what the emotions are or how many there are. Also, note that psychologists tend to define emotion in a narrow way, in particular referencing how transitory it is compared to moods or personality traits: https://en.wikipedia.org/wiki/Emotion_classification

So, you feel disgust and fear are different: I anecdotally agree, some models of emotion agree, and they do not have the exact same neural correlates.

Major theories of emotion generally classify emotions on two dimensions: approach vs. avoidance motivation, and pleasant vs. unpleasant. Fear and disgust are both avoid/unpleasant. Desire is in this sense the opposite of fear: approach/pleasant. An example of this model is explained here: https://en.wikipedia.org/wiki/Emotion_classification#Circumplex_model