I think the major point that people miss is that there is a thing called the "Carbon Cycle"[0] which basically stipulates that all carbon that already exists in the system will continually be transformed into different things and then back into carbon (and the inverse). This is pretty ordinary and cows are a part of that. Though the effects of transforming a lot of carbon at once might be profound and dangerous.
The major issue is that we're digging up shit loads of carbon and releasing it, which is the much more dangerous thing and reframing the argument to be against meat because meat has a carbon cost is like saying that the mountains are causing water levels to rise because "water comes from the mountains" (though, as part of the water cycle).
[0]: https://oceanservice.noaa.gov/facts/carbon-cycle.html