I would say $\infty - \infty=0$ because even though $\infty$ is an undetermined number, $\infty = \infty$. So $\infty-\infty=0$. 
From a layman's perspective, imagine that I have an infinite number of hotel rooms, each numbered 1, 2, 3, 4, ... 
Then I give you all of them. I would have none left, so $\infty - \infty = 0$
On the other hand, if I give you all of the odd-numbered ones, then I still have an infinite number left. So $\infty - \infty = \infty$. 
Now suppose that I give you all of them except for the first seven. Then $\infty - \infty = 7$. 
While this doesn't explain why this is indeterminate, hopefully you can agree that it is indeterminate!