I think the reason we eat turkey is because it's HUGE. A good sized bird can feed a large family and still leave some for leftovers. It's also relatively inexpensiove compared to other some meats and easier to find.
Supposedly, at the first thanksgiving they ate venison (deer) which is also very delicious and can last a while long after everyone has eaten their fill. However, venison is not often found in an American supermarket (or at an affordable price if so). In most cases, if you are determined to eat deer, you have to hunt it.... and not too many people these days seem to want to go to that kind of trouble.