If you were to watch the pendulum, you might be able to reliably make statements like "it's going to tip to the right in a few seconds" (particularly when it's near one of the bounds), but you won't be able to reliably predict which direction it will be tipped 3 minutes from now, or whether it will spend 8 seconds or 28 seconds tipped to the right, or whether its next 10 motions will be RLLRLRRRLL or RRRLLRLLRL. Any tiny error you make in measuring or predicting will be magnified over and over until the error is bigger than the signal/calculations.
We're all familiar with another chaotic phenomenon: weather. Tomorrow's temperature and prevailing atmospheric conditions can be predicted fairly well, but you can't make reliable weather projections more than a few days out. It's intrinsic to the system; a tiny effect like a butterfly flapping its wings half a world away is enough to make your predictions worthless a couple weeks out.