Why do veins have valves and why don't arteries have them?

The heart pumps the blood into the arteries with a very high pressure and the blood can therefore travel through them to the tissue of interest. The arteries are also very elastic, therefore they can pulsate and keep the blood flowing. Whereas the veins are collecting the deoxygenated blood from the tissues and sending it back to the heart. But the venous system has a lower pressure and therefore needs help to keep up the flow of the blood to the heart. The valves play an important role as the blood might have to flow against gravity (especially from the arms and legs). The valves in the veins prevent the backflow of blood and also help it move forward to the heart. An additional thing that works together with the valves are the muscles surrounding the veins, which help the blood to return to the heart when they contract.