No one is complaining about the carbon a cow is breathing in and out. It's the methane they produce, which is a very potent greenhouse gas, about 80 times the warming power.

Cows fart which creates methane. Methane is a much worse greenhouse gas than CO2. Like 25x worse. Add on to that we artificially increase the bovine population by orders of magnitude than they'd naturally attain so we can consume them. They contribute a lot to climate change.

Cows do not create carbon. They turn it into methane which is a worse form of carbon.

The same way you can turn carbon in biomass to "lock" it from the atmosphere, you can turn it in worse forms of gas that cause even more heating like methane. The methane will turn back in CO2 form once it burns or degrade naturally (a dozen years or so) but while it is under methane form, it will make it worse, accelerating the heating effects. But even stopping all methane emissions is only a temporary solution as carbon from pool 2 keeps moving in pool 1. It may give us more time before reaching the same level of greenhouse effect but we will reach it anyway.