Because that's the way to measure blood pressure
The German guidelines for treating hypertonia are to always measure bilateral. (German Source Only)
As @DoctorWhom pointed out in the comments, atherosclerosis1 and ascending aortic dissection2 can lead to difference in the blood pressure.
Furthermore, as a study fairly recently conducted (2012) found, not measuring bilaterally can have other devastating effects as well: An undetected difference in blood pressure greater than 15 mmHg increases the overall mortality by 60%, and cardiovascular mortality even by 70%. Furthermore, the risk of suffering from an undiagnosed PAD (peripheral artery disease)3 increases by factor 2.5.
The study concludes that
A difference in SBP of 10 mm Hg or more, or of 15 mm Hg or more,
between arms might help to identify patients who need further vascular
assessment. A difference of 15 mm Hg or more could be a useful
indicator of risk of vascular disease and death.
(Link to whole
Furthermore, the chances of a wrong reading are significantly lower if verified once.
1: Atherosclerosis is a form of arteriosclerosis where the artery wall thickens, thus leading to an increased blood pressure in this artery (and depending on the location, can lead to a difference between L and R blood pressure).
2: The aortic dissection is a tear in the wall of the aorta. As the tear extends along the wall of the aorta, blood can flow in between the layers of the blood vessel wall (dissection). This can lead to aortic rupture or decreased blood flow (ischemia) to organs. A decreases blood flow will result in lower blood pressure. Thus measuring L and R gives one a quick overview and a faster way of ruling aortic dissection out than sending the patient to the CT.
3: PAD's is a broad term for the narrowing of arteries different from coronary arteries and cerebrovascular arteries. Depending on the location of narrowing, a difference in blood pressure between L and R can occur).