For a while, I thought it was kind of silly to prioritize animal suffering because I consider a single human life to be worth more than a single animal life. The thing is, though, that there are so many more animals suffering for the same reason than there are humans suffering for the same reason that it is so much easier to identify and target a root cause that we can actually do something about.
Animal suffering exists in such astronomical amounts that it is an obvious place to look for opportunities to eliminate huge amounts of suffering in a single move. Moreover, such a move could even be called realistically attainable. For the purposes of this post, I will overlook wild-animal suffering, where it is more difficult to identify what should be done.
Each year, in the US alone, the food industry kills:
~42 million cows
~120 million pigs
~300 million turkeys
~452 million hens
~6 billion fish
~7 billion chickens
Passing legislation that affects even 0.1% of these 14 billion animals would still be reaching a staggering 14 million. On such a large scale, just making their lives 10% better would yield huge rewards without putting any farmers out of business (or even preventing them from getting rich). Even playing a small role in contributing to such an event would have more moral weight than the entirety of an average person's lifetime.
One way to ignore this conclusion would be to deny that animals are capable of feeling enough pain to deserve our concern. This is scientifically and philosophically unjustifiable, however.
Imagine a factory farm with a giant counter on top of it that keeps track of the amount of suffering going on under its roof. Every time a chicken stubs its toe - tack-tack-tack-tack, 50 points to Gryffindor! - the number on the counter rises in proportion to the amount of pain. When an animal gets killed, the number on the counter goes down slightly because that animal's suffering is reduced to 0. Now, imagine substituting all the animals inside the farm for humans, who must live in the same conditions and suffer the same fates. I claim that the number on that counter remains in the same general ballpark it was in prior to the switch. Maybe it even goes down because of the power of the psychological immune system to protect humans from depression.
If this is the case, then given the sheer numbers of factory farmed animals and given what they are put through, we are dealing with roughly a Holocaust's worth of suffering per year, in the United States alone. Given that the meat industry will continue to prosper indefinitely, we can expect multiple future Holocausts worth of suffering, again without counting any farming done outside the United States. Cutting out a tiny chunk of this suffering is still massive relative to almost anything else that can be done in a human lifetime. Contributing to a new law that makes animal farming more humane or deters meat consumption would be very effective.