The IMF's rules prevent the organization from lending to countries that cannot repay the loan. The IMF has concluded on the basis of facts and analysis that Greece cannot repay.  Therefore, the IMF is unwilling to lend Greece the money with which to repay the private banks.

The IMF says that Greece's creditors, many of whom are not creditors but simply bought up Greek debt at a cheap price in hopes of profiting, must write off some of the Greek debt in order to lower the debt to an amount that the Greek economy can service.

The banks don't want Greece to be able to service its debt, because the banks intend to use Greece's inability to service the debt in order to loot Greece of its assets and resources and in order to roll back the social safety net put in place during the 20th century.  Neoliberalism intends to reestablish feudalism—a few robber barons and many serfs: the One Percent and the 99 percent.