The statement, “Science fails to predict the weather” is one of those interested ways of conveying an idea by saying something totally untrue and meaning something completely different. A quick search of the web, tuning into television and radio, reading most newspapers, is a clear indication that science is actively predicting the weather.
Prediction, or forecasting, by definition is a best guess based on what is known and through the use of statistics, probability, and other methods. A prediction or forecast is almost never right; else it would not need to be called by those names. Science is therefore certainly not failing to predict, the real meaning behind the statement is that science is failing to predict within what people expect to be a reasonable confidence interval.
Weather is a very complex phenomenon with an enormous amount of variables involving fluid mechanics, thermodynamics, and many other forms of energy transfer. It is no easy problem to determine in advance what the weather will be. Just as it is not an easy problem to forecast how much inventory a company should hold, as demand can change due to many variables. The inventory problem is far less complex, yet the existence of scrap yards indicates that accuracy on a simpler scenario is also not exact.
If the experts in the weather industry were able to predict the weather with a hundred percent accuracy, they would no longer be in the industry. If science could predict the future with such accuracy, then it could be applied to the stock market too. Your evening weather announcer would do much better applying such forecasting skills to the stock market or solving other financial problems like forecasting demand patterns within supply chains.
Forecasting has improved over the years to some degree. With additional technology to collect data, and faster computers to process the data, the degree of accuracy has improved. It is still not dead on, but it is closer. The perception that science is always exact is not true.
There are two forms of science. When you add 2 + 2 you always get 4. When you add two parts hydrogen to one part water, you always get water. These are exact sciences, and what has caused the masses to believe science is always right.
There are non-exact sciences, psychology, medicine (yes, this is why people still die and why some medicines do not always work). Forecasting is another science that is not, nor by definition will it ever be, completely accurate all the time. On the other hand, there is a science that can determine the weather with complete accuracy all the time; it is called waiting until it happens and then recording the result.