Either "eating meat is fine because animal life is less valuable than people's dietary needs/preferences," or "vegetarianism is the only moral option, as all life is equally valuable," but it seems to me like any answer in the middle is hypocrisy, no?

I dug into this more deeply in another response, but no. Life can be equally valuable and we can accept that evolution and history has led us to a place where we end life without feeling a sense of superiority over that life.

Imagine a poker game. You have been dealt a winning hand. You are incredibly confident of this and are correct to feel so. Are you a better person for winning that hand? Is this a signal that you're not only expected to take the money of the others at the table, but permitted to do so because you are a better person?

We are the species that was dealt a better hand. This puts us in a position of power. This does not make us "better", nor does it negate the value of those other lives, despite the position we find ourselves in. Yet we do, ultimately, get to collect as a result of that hand.

If it would be a moral tragedy to kill a cat and eat it, why is that not true for a cow? If life eats life, it’s not murder for me to kill and eat the cat, correct? So why is it a moral evil if killing and eating the cow is not?

You may have misunderstood, or maybe I didn't word it clearly. There is no moral difference between killing and eating a cow or a cat, or even another human if need be but our society doesn't see it that way, and that's probably a good thing.

I think you’re saying that this is just one of the “fucked up” stances that society has taken? But then why participate in it?

It's quite difficult for one born in a society and living within a society's geographical bounds to just "not participate in it". I choose to not participate in parts as I am able. I am able to afford meat that is not produced in the factory farm system (i.e. crowdcow), and so that is one way.

but it seems to me like any answer in the middle is hypocrisy, no?

Yes, it's really nearly impossible to participate as a normal member of modern liberal society without being a major hypocrite. The more you try to not be a hypocrite, the more people think you're a weirdo.