The loss of sensation on the opposite side of the lesion is because the nerve fibers of the spinothalamic tract (which carry information about pain and temperature) crossover once they meet the spinal cord from the peripheries.
The phenomenon of losing sensation on the opposite side of a lesion can be attributed to the unique crossing pattern of nerve fibers in the spinothalamic tract, which transmits pain and temperature information. This occurs when these fibers cross over at the spinal cord level before entering it from the periphery.