P₁ It is wrong to inflict unnecessary suffering or to kill without a good reason.
P₂ Some non-human animals can suffer and be killed.
► It is wrong to inflict unnecessary suffering or to kill without a good reason some non-human animals.
Someone trying to dismiss the inclusion of some non-human animals on this concern could argue that they don't feel pain, they are not sentient beings.
I won't argue against this directly, because it is common sense and scientifically proven that at least some non-human animals can experience physical and psychological pain — e.g., cows, chicken, pigs, dogs, cats, etc. So this counter-argument may work for some kinds of animals, but for most of the animals that we exploit, this doesn't follow.
The other way to try to dismiss it, is by saying that that BV is poorly defined, that we don't know what it is meant by "unnecessary" or "without a good reason".
Well, we don't need to create a perfect definition of what "necessity" and "a good reason" mean in this context, we just need to know what people usually would think of as an unnecessary or bad reason for inflicting suffering or killing and to see if it also applies to the way we usually treat animals. What kinds of motives people would regard as unnecessary or as a bad reason for inflicting suffering or killing? All people would agree that inflicting suffering or killing for pleasure, amusement or convenience is wrong, or else they would be condoning rape, sadistic torture and slavery.
But most of the suffering and killing of animals is done for pleasure, amusement or convenience. For example, since we don't need to eat animal products to survive, it isn't necessary to inflict the suffering and killing that factory farms and other forms of animal exploitation usually require.
Thus, common sense morality implies The Basic Argument for Veganism. Just for the sake of clarity, we could rewrite it as follow:
P₁ It is wrong to inflict suffering or to kill any sentient being only for pleasure, amusement or convenience.
P₂ Some non-human animals are sentient, i.e., capable of suffering.
► It is wrong to inflict suffering or to kill non-human animals that are sentient, i.e., capable of suffering, only for pleasure, amusement or convenience.