You might be conflating what the common connotation of "intuition" is with the Jungian function "intuition". For example, a "woman's intuition" is hardly intuitive; it's a pretty strong evocation of Si. On the other hand, Jungian intuition means that the brain interprets sensory information as discrete parts as opposed to a concrete whole.
So,
Ne takes those discrete parts and handles them as they come, processed under whatever the judging function is (with Ti, trying to make those parts fit a logical whole, while with Fi, trying to categorize them according to normative determinations).
Ni takes those discrete parts and deconstructs them into further components, which are then reassembled by the judging function (with Te, attempting to create a different logical regimen from the same components, while with Fe, trying to understand how those components would work at various points within the social structure)
This is opposed to Se, which uses the entire block of sensory information, to either make a logical judgment (Ti) or normative determination (Fi), and Si, which deconstructs the entire block into what is most important based on that which has previously worked (Te) or what works within the social structure (Fe).