Technically we don't have to - but they have to be really, really recently deceased. Lobster and crabs decay so quickly after death that they present health risks if not cooked immediately.

Some people are not comfortable tossing what are essentially live bugs into a pot of boiling water, though, and there are debates on the most humane way to dispatch them. Some people plunge a heavy chef's knife into the back of the lobster's head, about an inch behind the eyes, to do them in before cooking. The same can be done for crabs. This method clearly kills them instantly, although they may continue to flop around for a bit - just as they do in the pot of boiling water. In our experience, it takes at least as much fortitude to kill them with a knife as to toss them in the pot.

If your question stems from humanitarian or vegetarian-inspired grounds, there is no getting around the fact that all the meat we eat was once alive and killed specifically for our consumption, whether we do the actual killing or not. And while very few of us have to slaughter a pig, cow, or chicken to feed the family these days, generations of our forebears did so. The only way to remove yourself from the actual process - though not the deed - of killing a lobster or crab is to purchase frozen lobster tails and pre-cooked crabs, or order them in a restaurant.