I feel a moral conviction not to do so, and I was wondering why it is permissible, as they are conscious, and it is just unnecessary torture and harm against innocent beings.
I've read through your replies and first I want to say thank you for caring about our fellows in nature. Unlike us, many of them nature has been their only teacher guide and mother; and mother nature is, a cruel mistress on purpose. How else do such monstrous powerful beings come to be without being forged in flames. Claws that rip and eyes to see in even 'the dark.'
For when you think about "mortality" you must understand this term is a bit strange, look for the concept of ethics first. From what can be seen morality as a whole is something only an advanced being can have because they don't need to "obey cruel physics" as much as we do. Morality would be if any God started murdering animals for the fun of it. They have the power freedom and even the spiritual authority to do so. Yet that would be wrong because just why, no need; thou art a God and thus have no need to do such things. Why waste such light on pettiness.
But humans? Especially in this age of the fallen, there is even "honor" to be gained from a great hunt because the values it takes to follow through with it are what make someone great. The knowledge and skill to provide for ones self is a very high ethic and something the Gods wish more than anything. Fail, fall, be broken; and get back up until it is so second nature that the Gods don't even need to push you in that direction. That is the starting of self sufficiency and it can be see in acts like hunting.
You track them down and learn what to do and not to do or else starve. Now yes you would likely cite "civilization" as to why there is no need, but this is merely the scabby remains of what can, was, and should be. You find yourself high and mighty but aren't yet stoic enough to understand so what at our level. If this means so much to you than grow to where the light of the cosmos is your food and find an animal to patron and love. Guide their evolution into becoming a more advanced being and see them blossom into a God themselves.
Freedom, Know Thy Self, Proportionality: these Ethics are very much needed here for such a discussion.
Freedom to know that you need to do what is needed to survive no matter what. If any creature needs to kill another to survive than the freedom to do so must be recognized. In this you can even have some form of pity on the nature of parasites. You should not care for them but understand they, like you, exist in this universe of duality and because freedom is meaningful to you; every action must take that into account. Look to our enemy that seeks not creation because they can not create. We do not scorn them for anything other than the fact they are bad for us. If they left us alone and stayed amongst themselves and never oppressed a creature of creation we wouldn't honestly need to care; but the very nature of a parasite is to cling and hold down another. Thus while you must understand why they are allowed to do it, you must also take a step back and see that your own freedom is to be protected at all times.
In this way an animal has the freedom to defend itself and thus to protect our own lives we have cultivated a place in the world in which both freedoms are not so trampled upon in a more golden mean than otherwise would exist.
A cow when properly cared for lives an existence in which it can evolve in safety. That payment for that is the end result of their lives that was going to happen no matter what, but it can be done with love care and honor. Say you do not wish to have a cow die by your hand, fine; but it's going to die and if not by our hands than by being ripped apart or some illness: what about that is some holy or special goal to you? Yes yes of course they have no other choice but that is the very point everyone is trying to make here.
Which leads into Know Thy Self. Know all of you, the good, the bad, and the ugly. Hate the bad, work on the ugly, and perfect the good; for to be human is enough. For what we are taught about being human is a false cold inhuman thing. You are not above the fray you exist with in it; and it is a glorious thing that pushes our evolution forward. Now granted you ask about Zeus which does lead into faith a bit but let me ask you this, if they had to suffer and rise up slowly and perform these kills themselves in their own time in their own world; than why should we not also suffer such a thing? Why are we not punished for it? Why even allow it in the first place?
Proportionality. You can not get the amount of good in a single bite of meat so easily else where. Sure you can say lab grown meat but if you've researched it at all you'd know it doesn't have an immune response and thus can not exist due to the "unseen world of microbes." They rule you far more than anything else. You gut is a prime example and shows us in many ways what we are like for the Gods. Small but meaningful on this plane. This sort of conceptual existence must always be taken to account because many things are just something else viewed in another way.
Justice is balancing the scales which is no different then having a golden mean of temperature. You can not have comfort without absolute zero and the literally endless amount of heat you can super charge into something. Which again is because of duality. If one has a bottom point than the other likely has no end cap outside of what naturally can exist without conscious effort being put into the system. Look to nukes, a flash of light that is literally what makes our own home star Sol/Sun exist and give us light and warmth; but placed here is literal destruction of the highest ordnances.
This is proportional though because even though it is a flash of death here, far enough away it gives light and warmth and wonderous energy for us to suckle upon no different than our mothers. If this is our home star given us such a lesson than it must truly be special in the energy that exist around us.
And what is that lesson? To be human is enough. Always and forever it is literally enough. It is human to eat animals because we did so before we could live without them and thus our bodies, and maybe even our souls, are attuned to it and wanting for it because it grew up on it. That pain you feel though is wonderful and human. Embrace it by being thankful and advocate for humane slaughter.
Trust me, the want to whine is known by many here and they overcame it. Look to our Mystical Holy Wonderous High Priest who grew from an angry cobra commander into someone I believe Plato would call his dearest friend. He was always wiser and more chosen than others but even he grew. He used Ethics to better himself to the point his past self is not visible. Just like how inside you exists a snake in both body and soul yet is unseen without effort.
Use your emotional drive for positive effort because boundaries exist and that is why we use our freedom to press against them endlessly. Nature might say I have to eat animals but I'm going to "one up her" and provide a place in which we can exist in a state of the most golden mean; outside of that, all effort is wasted. Thus a goal is seen, and must be set.
I'm very proud of you for caring about them so deeply but know that just like our love of pleasure, it can be used against us. Always, first and foremost; protect yourself and find others who care about self protection. That is how a real community exists and thrives. Look only to what it means to be loyal and a friend. If someone very self interested now has in their mind you being a part of their self interest, what more proof do you need you could trust them. This goes for the animals that live around us and our fellow human. For an animal we see in our self interest their self interest and thus we can be fast and good friends so long as respect and understanding is shared here. After all you know if a cow likes you or not and if you've never seen how they react to a farmer than you have no idea what they really feel. They love the farm how is good to them and loves them and that is why you must advocate against anything but humane golden mean life styles for all involved.