A vegetarian who keeps a carnivorous pet might encounter a dilemma : such as described in a (forthcoming) paper for the journal Appetite. ‘A meaty matter. Pet diet and the vegetarian’s dilemma’ The author, Dr. Hank Rothgerber, from the Psychology faculty at Bellarmine University, Louisville, Kentucky, US,
“… specifically focused on the conflict that pits feeding one’s pet an animal-based diet that may be perceived as best promoting their well-being with concerns over animal welfare and environmental degradation threatened by such diets, here labeled the vegetarian’s dilemma.”
The survey of 515 non-meat-eaters showed that :
“Vegans and those resisting meat on ethical grounds were more likely to feed their pet a vegetarian diet and expressed the greatest concerns over feeding their pet an animal-based diet.”
But, aside from the dilemma posed to the pet owner, is a long-term vegetarian diet nutritionally suitable for a carnivorous creature? It may depend on the animal. For an example study, see: ‘Evaluation of cats fed vegetarian diets and attitudes of their caregivers’ (J.Am.Vet Med Assoc 20 06;229:70–73) But for so-called ‘obligate’ carnivores, say snakes, it might be problematic (though as yet there don’t appear to be any scholarly studies on vegetarian snakes.)
Dr. Rothgerber has also authored other vegetarian themed papers: e.g. ‘Real Men Don’t Eat (Vegetable) Quiche: Masculinity and the Justification of Meat Consumption’. (Psychology of Men & Masculinity, Nov 12 , 2012)
Further reading :
 “Why consider a vegetarian diet for your cat?” from the Vegetarian Society.
 Vegetable Philosophy from the University of Guelph, Canada.