Why arrays more than 3D are harder to manage?

Answer 1

Because it's easier to overlook a position in the array and also needs more loops inside other loops to iterate through the whole array, it becomes kind of a mess of loops tangled into each other making things more complicated than they need to be.
Actually I wouldn't even recommend a 3D array unless it's truly necessary and such a case will rarely happen if at all

Answer 2

imagine, a 2 d object(stick man)
now imagine, a 3 d object(chair)
obviously a 3d object is much more complex than a 2d object

most of the time 2d arrays fulfill your needs.
as of today I haven't used any 3d arrays

Answer 3

You can imagine a 3D cube like rubiks cube. now you add a color to each small cube: thats 4D. You can continúe adding a material or what you want to get 5 or more dimensiones. The point is that the human brain is used to think in max 3 dimensions.