Fuzziness means illogic ?
There is a particular logic (“Classical Logic”) that people are usually thinking of when they mention logic. Many folks don’t know that there are many, many logics that have been invented by mathematicians and philosophers, and an infinity of possible logics. All are as mathematically sound as each other. They vary in how truth behaves (SQL’s true-false-null is a poor attempt at a 3-valued logic, for example; or you might include notions like necessity and possibility or time).
Fuzzy logic is another logic. It’s quite precise about how truth behaves, and truth is a real number on the range [0, 1]. And it does a nice job of providing a notion of partial truth.
Unlike boolean logic where you're either "tall" or "not tall".
Using your example, if the control system can utilize non-binary, numerical input and do something with it in actuators, then just give it the actual height (in cm). If it can't, then introducing the concept of "semi-tall" isn't going to be helpful.
The example we learned in class is the classic thermostat of an air conditioner. Sure, it would be nice if it can tell between cold, warm and hot instead of a binary 0 and 1, but why not just use the actual numeral value (0.1, 0.22, etc.) then?
The aircon example isn't really that great, to be honest, because there's only one rule and only one action you can take. If you add in "how full is the room" (and letting that be tuned for room size), an automated window vent, the outside temperature, and some sort of air quality reading, you can see how the job of making a room tolerable to be in starts to combine factors in interesting ways. https://en.wikipedia.org/wiki/Fuzzy_associative_matrix and https://en.wikipedia.org/wiki/Defuzzification are things I'm sure your course would have covered, but that's where I'd point at as a start.