Whatever we tax, we discourage. Sometimes that's a necessary cost (like for an income tax), sometimes that's a desirable outcome (like a cigarette tax). Rapid automatic trading is something we want to discourage -- it can lead to run-away price swings, and it locks little investors out of the gains. A small tax (like 0.1% of a transaction) will not have any significant effect on individual investor transactions, where it's tiny compared to the fees we all pay.
See http://www.nationalnursesunited.org/pages/financial-transaction-tax for more in-depth arguments.