If climate models were predicting the temperature of your city on March 21, 2120 then your intuition here would be wise. But that is not at all what these models are predicting. They are predicting global average annual temperatures and other gross, planet-scale statistics.
"Average annual global temperature in a given year" and "temperature in my city tomorrow" are fundamentally very different types of predictions.
Often it is easier to accurately forecast gross dynamics on a long time frame than it is to forecast precise dynamics the exact same process over a short time frame.
You don't even need to understand the math or physics to see why this is intuitively true.
Consider e.g. predicting minutiae about the behavior of a fetus over the next week ("how many fist clenches", "how many kicks") vs. predicting which week the baby will be born -- the latter is substantially easier than the former despite the longer time frame.
Or, more to the point, consider forecasting the position of a particular cloud of molecules in a pot of water being bought to boil vs forecasting the temperature of the water in the pot in 5 minutes. The latter is hilariously trivial -- a small child can be taught how to do this with excellent accuracy. The former is some horrendously difficult phd level fluid mechanics and even then hard/impossible.
In some sense, an educated intuition is exactly the opposite of yours -- it'd be surprising if we were this good at extremely fine-grained weather prediction but couldn't guess the annualized average temperature of the entire system in 50 years. The latter is a much simpler statistic because the timescales and physical scales take a lot of the difficult stochasticity out of the forecasting problem.