For the same reason burning wood is green- as long as you are regrowing it.
So - if you're burning timber from a forest which is sustainably managed (so you're renewing wood at the same rate you're using it), then there is no net carbon released.
That would be true if carbon dioxide was the only greenhouse gas. But it isn't.
Burning biomass could be sustainable if we make sure that new biomass is grown at the same rate as it is burned. I have yet to see a document assuring me that is the case.
In any case burning biofuel is not greenhouse gas neutral. And hence not green.
So - if you're burning timber from a forest which is sustainably managed (so you're renewing wood at the same rate you're using it), then there is no net carbon released.