"Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.[6] This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution[7] and is fully determined by their initial conditions, with no random elements involved.[8] In other words, the deterministic nature of these systems does not make them predictable."
On top of this some systems are not only sensitive to initial conditions but actually generate randomness (or destroy order, depending how you look at it), such as class-3 cellular automata.
afaik the point with chaotic systems is that even if the system is deterministic and your measurement of the initial conditions is near-perfect, your predictions will diverge from the real thing pretty quickly, because any errors get magnified a lot
If you try looking at finer and finer details, you'll quickly run into quantum effects and the uncertainty principle. If even the smallest parts of a system aren't deterministic, how can the outcome be predicted?
"Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.[6] This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution[7] and is fully determined by their initial conditions, with no random elements involved.[8] In other words, the deterministic nature of these systems does not make them predictable."