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