It is not just the number of variables; it is also the underlying equations.
The atmospheric models rely on non-linear equations. Even non-linear equations with only three variables can be unpredictable. With these equations, small errors are amplified, such that two simulations starting with small differences will have diverging results after a period of time. And one can never measure to the accuracy needed to make truly long-term predictions.
What amazes me is that the climatologists should know this, unless they really don’t understand the mathematical nature of the equations they are trying to solve.
I suspect, but I am not positive, that most climatologists are not mathematicians or programmers. They “consult” others for those details. There were a number of times in my own career that I programmed complex mathematical equations that I really didn’t understand, even though I have a decent math background. I did rely on mathematicians to test and verity the accuracy of my work, but they had no idea what I programmed. It was a black box to them. I suspect there are a lot of black boxes involved in climatology and no one person understands what’s inside all of them.