Let me put it my way:
When a plumber puts his knowledge and tools to work, his revenue is taxed once, at personal level.
When a shareholder puts his knowledge and money to work (along with other shareholders, in form of a company), his revenue is taxed at both company level and again at private level.
Can you spot the double taxation now?
The philosophy here is that you shouldn't get taxed on dividends because you're an owner... the money was already yours. The plumber didn't have to pay tax again to take his money out of his plumbing business (maybe a limited-liability partnership) and buy DVDs, but the shareholder did.