The supply of herd animals very obviously isn't fixed. Humans breed them for resources, and since the world population has more than doubled over the last 50 years, the supply of herd animals has also increased a lot. If humans stopped breeding cattle for resources, there'd be far less cattle.
The amount of atmospheric methane also very obviously isn't fixed. Increases in production result in a higher concentration of methane, since it takes ~a decade to break it down. As long as you keep increased output of methane, the baseline concentration will also stay increased.
Your point about "kill[ing] all of them and bury[ing] their carcasses underground where they can’t decompose" also shows that you really don't understand that 1) different animals produce different greenhouse gases that may have weaker or stronger effects, and 2) that we're actively causing far more cattle to exist than would without us continuously breeding them.
The only way I can see your points making sense is if you're literally approaching the topic from an absolutist binary perspective (as in, "either we keep going exactly as before, or we have to literally kill all animals, no middle ground possible").
The amount of atmospheric methane also very obviously isn't fixed. Increases in production result in a higher concentration of methane, since it takes ~a decade to break it down. As long as you keep increased output of methane, the baseline concentration will also stay increased.
Your point about "kill[ing] all of them and bury[ing] their carcasses underground where they can’t decompose" also shows that you really don't understand that 1) different animals produce different greenhouse gases that may have weaker or stronger effects, and 2) that we're actively causing far more cattle to exist than would without us continuously breeding them.
The only way I can see your points making sense is if you're literally approaching the topic from an absolutist binary perspective (as in, "either we keep going exactly as before, or we have to literally kill all animals, no middle ground possible").