The reason is that you flood the fields with slowly moving water that drowns the weeds and lets them rot, while you plant seedlings by hand. The rotting weeds produce methane gas (as do the water buffalos but that's another story).
You can also grow rice by just throwing seed down and letting it grow, as is done for the dry season on low lying fields.
more details at the rice project site here.
Then we read: this: Oh my, maybe that's why the ice age hasn't returned:
It has been hypothesized by some climate scientists that methane from rice contributed to an anomalous rise in methane over the past 5000 years which is not explained by natural sources. If so, then this has contributed to global warming even before the industrial era and will need to be factored into models that hope to predict where global climate change is going.
one way, of course, is GM modified rice, but never mind: The anti science types would rather have Asians starve than admit science can benefit humanity.