Consider a macroscopic canister filled with a classical gas (comprised of elastic molecules bouncing around and obeying Newton's laws). Suppose that at some time I gave you the positions and velocities of every single molecule in said gas to within one part in 10^-20. Though you might be able to predict the positions and velocities of every molecule for a short period of time, you would find that your prediction diverges exponentially from the true result, even though the error was initially tiny and you understood all of the dynamics in the system. Such sensitivity to initial conditions is the essence of chaos theory. Weather is a chaotic system, and you can only predict it a few days out without requiring exponentially more resources (i.e., sensors and computing power).
So, does this mean that all of fluid dynamics is bunk? What about pV = NkT? After all, if it's impossible to predict the future behavior of the gas molecules, how can we say anything about the gas? The reason you can make statements about pressure, volume, etc. is that these are bulk quantities, described by global constraint equations (e.g., conservation of energy, conservation of particle number, etc.). Climate, too, is a bulk quantity governed by global constraint equations, especially conservation of energy. Casting doubt on macroscopic climatology simply because it is impossible to make "microscopic" predictions shows a profound lack of understanding of physics.