Because in some states, Texas for example, the Living Will allows you to do two things prior to being in a terminal or irreversible condition where you can't make your needs known:
Say what kind of care you would like you would like;
Say whom you would like to make choices for you
See that last thing, "Say whom you would like to make choices for you." Well, the little clause where it allows you to say who makes choices is not really very strong. In most cases you'll be just fine filling it out. But, in families where people have very different opinions about values, ethics, then the whole thing can end up in court faster than you can blink an eye. When that happens, trust me, you'll want a Medical Power of Attorney.
Now, why would that be the case? Because the Medical Power of Attorney (MPOA) spells out everyone's obligations really clearly - the doctor's, the person you name as your agent, your responsibilities - everyone's. And when you end up in court, if you don't have the strongest possible support for your views, guess what? You may well lose and have exactly the care you didn't want.
Now, here's another neat little part of this whole package. If you have BOTH the Living Will and the Medical Power of Attorney, you agent is obligated to follow ALL your choices and values as expressed in that Living Will. If they don't THEN they can be legally removed as your agent. If a doctor doesn't follow your wishes, they must refer you to another doctor who will. So, take our non-legal advice - GET BOTH!