Your conclusion may be true but your examples aren't. You can definitely predict the stock market based on past prices, and I suspect you can with weather as well.
This is only true if you consider occasionally doing slightly better than random chance, "predicting the stock market". Unfortunately, while this would be enough to make a trader a net positive return over time, we have more stringent requirements for a system to become AGI.
> I suspect you can with weather as well
You suspect wrong.
If you are talking about the overall climate, that's a different thing, and we can, because we abstract away sufficiently much that emerging patterns are averaged out.