I could explain it, but I would need charts and graphs and an easel. (I am being sarcastic).
From an engineering stand point the biggest problem is the pressure and speed at which the oil is rushing upward. The upward pressure can sheer/bend metal--think a sort of oily fluid knife. Add to that hazard, the fact that the leak is under essentially a mile of water. Finally the biggest problem, the oil has value.
There is a pretty easy effective way to stop the oil flow, but it would mean making the oil unable to be collected in future. The Russians used low level nuclear weapons four or five times when they had out of control natural gas mines. The value of the oil, prevents the destruction of the well.
**I am not a big nuclear advocate, however I am also not a fan of dead and oil coated wildlife.