In short:

Because everyone can buy a share just at the end of the day before the dividend "ex-date" and sell it at the beginning of the next trading day while having gained the right to receive the full dividend.

So if the share closes at $100 and gives you a $5 dividend, if the share open at $100 every bozo on earth could earn $5 by buying then selling without taking any risk. So in practice, the share opens at $95.

For the shareholder: before $100 in one share, after $95 in one share and $5 in cash. Zero gain.

If you don't believe me, look at my french blog example: when microsoft paid a total $30 billion in dividends on the week-end after friday 12 november 2004. Shareholders gained next to nothing.

When dividends are paid, the share price is depressed in proportion to the size of the dividend, so the shareholder breaks even. If the dividend is paid in cash, the shareholder can buy shares with it, and if it's paid in shares the shareholder can sell them for cash. Or the shareholder can obtain a dividend even if the company doesn't give it out by, say, selling a few percent of his/her holding each year. It all boils down to the same thing.