Why do weathermen and amateurs use green screens when professional movie makers use blue screens?
Professional film productions use neither only green nor only blue for chroma keying, but switch between both depending on the scene. Each can only be used when there are no objects of the same colour in view, otherwise it takes extra work to un-remove these objects. Blue and green are the usual colours because the human skin, which is what will almost always need to remain visible, is very different from both, but this is not the only thing shown in chroma key scenes!

In most situations, you have neither blue nor green objects in the foreground so both colours will, in principle, work. But they may not work equally well. The main reason why green is predominant in digital productions: digital cameras can resolve green light best, so it's possible to do proper green chroma-keying even with a cheap camera that might have problems to resolve a blue screen accurately enough. But that's not a concern in professional film productions. Analog cameras actually resolve blue better, but the difference is not really significant.
Especially blond hair will sometimes reflect much of the light coming from a greenscreen behind, which can lead to weird and somewhat ill-looking green shades. Blue is less problematic in that aspect. On the other hand, clothing will more often feature blueish colours than greenish ones.