The question is less of why you "should" and more of why you would want or need to. If you like to develop interesting presentations, animations, Flash movie clips, web page components, exported graphics such as vector icons, convert movie clips or simply create a joke application (these are only a few ideas that I have developed in the past), then Flash is merely the tip of the iceberg.
However, it is not so difficult learning the program itself, it is quite simple to understand and easy to navigate the tools... it is the ActionScript you will want to learn because it is very powerful and can accomplish far too many things to mention. Knowing ActionScript completely is seemingly impossible, but the scripting engines are regularly updated and expanded, and getting more versatile every day to accomplish from basic to professionally implemented complex tasks.
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