If it is a given that man is an animal, as is so famously articulated in Aristotle’s famous dictum that man is a social animal, then there should be no good reason to exclude ideas which, in general, are meant to apply to man as an animal, from animals. So in the case of vegetarianism: if there is an argument suitably argued against vegetarianism for animals qua animals then it will apply to man insofar as he is an animal as well.
This is the case in an interesting passage from the first book of Aristotle’s Politics.
For some animals, when they are created, at the outset bring forth with them in the process of creation (τοῖς γεννωμένοις) so much nourishment as is adequate until the time when the animal itself is able to provide for itself; for example those animals which have larvae or eggs. As many animals as give birth to live young, they have nourishment in themselves for a given time, the substance called milk. So that clearly one must think that [there is nourishment] for the things which have been created (γενομένοις), plants on account of animals and the other animals for the sake of humans. The tame animals are for the use and nourishment of mankind, while the wild ones, if not all, most of them, are on account of nourishment and help, in order that clothes and other tools come to be from these. And therefore, if nature does nothing in vain or without a purpose, it is necessary that nature made all of these on account of humans (Translation mine, Aristotle, Politics, 1256b10-22) 
Aristotle, not uncharacteristically, is running together lines of thought, arguments and assumptions. He begins from the idea that in nature when an animal is in the process of being former, it is supplied by nature with some form of physical sustenance, such as an egg providing not only a type of shelter but also some nutrition for the growing embryo. To Aristotle, this is a universal feature for animal life; even in the case of animals which give birth to live young, their mothers are capable of lactation to provide this same sustenance in a different manner. Thus, the thinking goes, when an animal is past the initial stage of life, nature would likewise still provide it with nourishment as when it has reached the point of maturity.
Latent within this passage is the idea that once nature has delivered an animal into its full physical maturity, it will have come to possess capabilities to procure food by its own means. Thus, there is still a need for food, but the initial form of food, such as a lactating mother, is not longer present for the animal. The animal feels the urge to continue feeding, and in Aristotle’s mind, it has a natural instinct to seek those things which will best suit its appetite. Among those things are both plants and animals. Thus vegetarianism is ruled out, albeit Aristotle does need some detail work in explaining the nuances of this idea in full.
Lastly, there is the point made about nature doing nothing in vain. What does he mean in applying that thought in this case? (1) Either that nature does not bring an animal into maturity to just let it die since it has no way to get food (e.g. a human baby dies because it cannot find food); but this would be absurd. (2) Or nature does not bring an animal into existence for it not be used in the proper way (i.e. cows are made for hamburgers, for leather, and for milk) (3) Or both, to put it somewhat directly, the predator and prey are made for a purpose, and both fulfill their roles.
 καὶ γὰρ κατὰ τὴν ἐξ ἀρχῆς γένεσιν τὰ μὲν συνεκ- (10)
τίκτει τῶν ζῴων τοσαύτην τροφὴν ὥσθ’ ἱκανὴν εἶναι μέχρις
οὗ ἂν δύνηται αὐτὸ αὑτῷ πορίζειν τὸ γεννηθέν, οἷον ὅσα
σκωληκοτοκεῖ ἢ ᾠοτοκεῖ· ὅσα δὲ ζῳοτοκεῖ, τοῖς γεννωμένοις
ἔχει τροφὴν ἐν αὑτοῖς μέχρι τινός, τὴν τοῦ καλουμένου γά-
λακτος φύσιν. ὥστε ὁμοίως δῆλον ὅτι καὶ γενομένοις οἰη- (15)
τέον τά τε φυτὰ τῶν ζῴων ἕνεκεν εἶναι καὶ τὰ ἄλλα ζῷα
τῶν ἀνθρώπων χάριν, τὰ μὲν ἥμερα καὶ διὰ τὴν χρῆσιν
καὶ διὰ τὴν τροφήν, τῶν δ’ ἀγρίων, εἰ μὴ πάντα, ἀλλὰ
τά γε πλεῖστα τῆς τροφῆς καὶ ἄλλης βοηθείας ἕνεκεν, ἵνα
καὶ ἐσθὴς καὶ ἄλλα ὄργανα γίνηται ἐξ αὐτῶν. εἰ οὖν ἡ (20)
φύσις μηθὲν μήτε ἀτελὲς ποιεῖ μήτε μάτην, ἀναγκαῖον
τῶν ἀνθρώπων ἕνεκεν αὐτὰ πάντα πεποιηκέναι τὴν φύσιν.
 Unsurprisingly, Aristotle will include hunting among the means.