Vegetarian has the roots:
vegetare (from Latin) + -arian (Latin -arius, meaning having a concern or belief in a specified thing.)
Pescatarian has the roots:
Piscis (from Latin), which is the root for the Italian, pesce and the -tarian pattern from vegetarian
Considering the Latin for meat is cibum, which forms carnis (think carnivore, carnage, etc) it follows that a meat-eater should be carnitarian, from carnis and the same -tarian pattern from vegetarian and pescatarian. However, this implies a diet exclusively of meat, which is not the desired word. Therefore one should consider:
Omnitarian, from the Latin omnis meaning "all; of all things."
Obviously these seem to follow the pattern of carnivore and omnivore, which already fit this meaning and are therefore redundant. Ultimately there isn't any point in making up omnitarian, and it's highly unlikely to catch on - but still, should someone require it, it does make sense!
Definitions from the Google dictionary, which I believe is from the Oxford.