Why are fractal curves nowhere differentiable?

I am a highschool student who stumbled upon fractals when doing a math project. In my research about fractals, I have found that they are nowhere differentiable. Can someone explain this in simple terms? Especially if the Koch Snowflake was used as an example to explain. Since this is the fractal I am most familiar with.

As I have understood it, since fractals have infinite iterations, the distance between two points can never decrease, only increase. However, in derivation, the distance between those two points, h, goes towards 0. Hence, this is not possible in fractal curves, even if they are continuous.

Feel free to laugh at me if I am completely wrong.

Differentiable functions are locally "linear-like". Zoom in and function and tangent will be more and more similar. The self-similarity of fractals gives inexhaustible detail at all scales.

Geometrically, differentiation is finding the slope of curve. for example the slope of absolute value function $|x|$ at 0 from left is $-1$ and from the right is $1$, therefore it's not differentiable at $0$. see the picture

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