> Matter is not continuous and yet we don’t need atoms to predict how a metal sheet will bend.
At sufficient detail atomic structure has a huge impact on how a metal sheet bends. Metallurgy seriously investigates at this level.
Hand waving details is fine when discussing with friends, it’s not a sound foundation for serious academic research.
Also, the degree to which the weather is unpredictable 2+ weeks out is somewhat overblown. It generally snows in DC several days a year yet the odds it snows in DC 2 weeks from now is essentially zero not ~4/365. Similarly you can more accurately predict thunderstorms than a pure guess 2 months from now. We may call it climate, but a physical model of earths tilt, prevailing winds, CO2, etc is better than just historic data.