Why Are We Exporting Ethanol?

Why are we exporting ethanol to Brazil, of all places?  I don't get this:

Ethanol demand is up as much as 6 percent this year over 2010, largely due to exports to Brazil and Europe that are expected to top 1 billion gallons.
Most ethanol plants are operating in the black despite corn prices that reached above $7.40 per bushel last week. High gasoline prices this year have made it economical for refiners, pipelines and other wholesalers to blend cheaper ethanol with gasoline.
“The whole commodity complex has gone up in sync during the last year, and as long as there is a favorable spread between ethanol and unleaded gasoline, we will be able to make our margins,” said Jim Gillingham, senior vice president for alternative energy of Texas-based Valero Energy as he toured Valero’s 110-million-gallon ethanol plant at Albert City.

Brazil grows sugar cane and makes ethanol out of it.  Why are we using corn to make ethanol, then exporting it to Brazil?  I don't understand that at all.  Even more so, why are we subsidizing production of ethanol if we are going to export it?  Food prices are going up because we need to make fuel for Brazil?