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.