Why is the blood pressure in pulmonary artery higher than in pulmonary vein?

The Artery is leaving the heart and so the blood within it is being pushed hard enough to make the blood further along the circulatory system return to the heart, therefore any arterial blood is going to be at a greater pressure than any venous blood (pressure is lost due to the vast number of branches to the system along the way).
Although venous blood is de-oxygenated, one of the few exceptions is the pulmonary vein which delivers oxygenated blood to the heart.