I don't understand why SolidWorks is unable to create this swept cut. Please help.
Probably because the cut would intersect itself when it comes back around. I'd suggest making the cut in two steps: a simple Cut-Extrude and then a Cut-Revolve. I'd post my part, but I edited it with SW2015 so you wouldn't be able to open it.
Here is a sample file with Glenn's method.
Here is how I did it.
You can also use the Solid Sweep Cut.
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