Taking one, leaving one

They're removing a tree from across the street.  But not the one that lost the big branch that crushed a van, a car, and damaged a truck.  However, they will be removing the dead wood from it.  I can't understand how they can leave that tree on the right.  With that big scar on the side where that large branch used to be, I just can't see how that tree can be healthy enough to remain. 
This is just another job done in the neighborhood that I wasn't consulted on beforehand.  Go figure!