If we cannot predict the weather next week, how can we predict the climate over the next century?While this sounds like a reasonable argument, there are in fact good reasons to accept 100-year climate forecasts even though we cannot predict the weather more than a few days out.
Predicting the weather is hard because you have to get the exact details of a weather system right. If your prediction of a storm track is 100 km off, then a giant snowstorm predicted to bury a city might fall harmlessly offshore. If your temperature is 3 deg C off, then what you predicted as rain turns into snow. If your initial conditions are off, then precipitation predicted to fall during rush hour falls at midnight. All of these things mean that you've blown the forecast, and people will mumble about how weather forecasters don't know what they're doing.
For the climate, these things generally don't matter. What matters is that, in the long run, one gets the statistics of the weather right. If one storm in a climate model is 100 km too far East, that won't matter if the long-term statistics of the storm track is right. This is quite a different problem than predicting the EXACT evolution of a single atmospheric disturbance.
One simple way to think about the difference in predicting weather and climate is to think about rolling a six-sided die. Predicting the weather is like predicting what the next roll will be. Predicting the cliamte is like predicting what the average and standard deviation of 1000 rolls will be. The ability to predict the statistics of the next 1000 rolls does not hinge on the ability to predict the next roll. Thus, one should not dismiss climate forecasts simply because weather forecasts are only good for a few days.
One should not take from this that climate modeling is easier than weather forecasting. There are several aspects of the problem that make climate modeling more difficult than weather forecasting: climate models need to also predict the evolution of long time-constant domains like the oceans, cryosphere, and biosphere. Weather models don't have to worry about these things because oceans conditions, etc. don't change over a few weeks. Climate models also use uncertain predictions of future emissions, from which the atmospheric concentration of CO2 and other greenhouse gases will be determined.
Another statement you hear is that:
Because climate models do not predict next year's climate, why should you believe a prediction in 100 years?Here's why: short-term forecasts (e.g., over the next few years) require accurate simulation of the magnitude and phase of short-term climate variability like El Nino. Over much longer time scales, however, one does not need to accurately simulate these short-term climate variability. I discussed that here. The upshot is again that one should not dismiss the long-term climate forecasts because short-term forecasts are problematic.